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1 Chapter Famil and Communit Involvement (English) Famil and Communit Involvement (Spanish) Section Section Section Section Section Section Section Cumulative Review Algebra 1 Copright Big Ideas Learning, LLC

2 Name Date Chapter Writing Linear Functions Dear Famil, Selling refreshments is an eas wa for a club to make mone at a school event. You or our student ma have volunteered our time to work at a refreshment stand. Suppose ou are working at a school carnival. Because the peanuts were donated, all sales are profit. The cash bo starts with $30.00 for making change. You can figure out how much mone should be in the cash bo with a linear equation. Amount in cash bo Peanut price Peanuts sold = Initial amount + (per pound) (in pounds) = 30 + Make a table of values. Find the value of if is 1, 1.5,,.5, 3, 3.5,,.5, and 5. What do ou notice about the slope of the line? What does the slope represent? Suppose our parent gives ou $10 to spend on peanuts with a group of friends. The amount of mone remaining depends on how man peanuts ou and our friends have alread purchased. Profit from Peanuts Peanuts (pounds) Cash bo (dollars) Peanuts price Peanuts bought Amount remaining = Initial amount (pound) (pound) = 10 Make a table of values. Find the value of if is 0,.5, and 5. Graph our points on a coordinate plane. How is this graph different from the first graph? Eplain. Eplain what the points (0, 10) and (5, 0) represent. Enjo our peanuts! Copright Big Ideas Learning, LLC Algebra 1 113

3 Nombre Fecha Capítulo Escribir funciones lineales Estimada familia: Vender refrescos es una manera fácil para que un club recaude dinero en un evento escolar. Usted o su hijo podrían haber ofrecido su tiempo para trabajar en el puesto de refrescos. Supongan que están trabajando en una feria escolar. Como los cacahuates se donaron, todas las ventas son ganancia. La caja registradora comienza con $30.00 para tener cambio. Pueden saber cuánto dinero debería haber en la caja registradora con una ecuación lineal. Precio de los Cacahuates Cantidad en la caja registradora = Cantidad inicial + cacahuates vendidos (por libra) (en libras) = 30 + Hagan una tabla de valores. Hallen los valores de si es 1, 1.5,,.5, 3, 3.5,,.5 5. Qué observan sobre la pendiente de la recta? Qué representa la pendiente? Supón que tu padre te da $10 para gastar en cacahuates con un grupo de amigos. La cantidad de dinero que sobre depende de cuántos cacahuates a han comprado tú tus amigos. Caja registradora (dólares) Ganancia de los cacahuates Cacahuates (libras) Precio de los Cacahuates Cantidad que sobra = Cantidad inicial cacahuates comprados (libra) (libra) = 10 Hagan una tabla de valores. Hallen el valor de si es 0,.5 5. Hagan una gráfica de los puntos en un plano de coordenadas. En qué se diferencia esta gráfica de la primera gráfica? Epliquen. Epliquen qué representan los puntos (0, 10) (5, 0). Disfruten los cacahuates! 11 Algebra 1 Copright Big Ideas Learning, LLC

4 .1 Start Thinking In order to graph a linear equation in slope-intercept form, what do ou need to know? What does the equation look like when the -intercept of the line is equal to 0? What does the equation look like when it also has a slope equal to 1?.1 Warm Up Graph the linear equation in a coordinate plane. 1. = 3 +. = 3. = 1. = 5. = + 6. = Cumulative Review Warm Up Determine whether the table represents a linear or nonlinear function. Eplain Copright Big Ideas Learning, LLC Algebra 1 115

5 Name Date.1 Practice A In Eercises 1 3, write an equation of the line with the given slope and -intercept. 1. slope: 3. slope: 3. slope: 0 -intercept: 8 -intercept: 0 -intercept: In Eercises and 5, write an equation of the line in slope-intercept form.. 5. (0, 3) (, ) 6 (3, 5) (0, 1) In Eercises 6 8, write an equation of the line that passes through the given points. 6. (, 3 ), ( 0, 9 ) 7. ( 5, ), ( 0, ) 8. ( 1, ), ( 0, ) In Eercises 9 11, write a linear function f with the given values. 9. f( 0) = 3, f( 1) = f ( 0) = 9, f( ) = 11. f() f () 1. In 003, a gallon of gas cost $1.75. In 013, a gallon of gas cost $3.50. a. Write a linear model that represents the cost (in dollars) of a gallon of gas as a function of the number of ears since 003. b. Use the model to predict the cost of a gallon of gas in Line is a reflection in the -ais of line k. Write an equation that represents line k. 3 =, 0 = 1 (, 5) (0, ) 116 Algebra 1 Copright Big Ideas Learning, LLC

6 Name Date.1 Practice B In Eercises 1 3, write an equation of the line with the given slope and -intercept. 1. slope: 3. slope: 0 3. slope: 5 -intercept: 9 -intercept: 1 3 -intercept: 7 In Eercises and 5, write an equation of the line in slope-intercept form (0, 0) (0, ) 3 (, 3) (3, ) In Eercises 6 8, write an equation of the line that passes through the given points. 6. (, 0 ), ( 0, 7) 7. ( 0, 3 ), (.5, ) 8. ( 0, ), ( 6, 1.5) In Eercises 9 11, write a linear function f with the given values. 9. f( 6) =, f ( 0) = f( 0) = 1, f( ) = f( ) f ( ) 1. A T-shirt design compan charges our team an initial fee of $5 to create the team's design. Each T-shirt printed with our design costs an additional $8. = 3, 0 = a. Write a linear model that represents the total cost of purchasing our team s T-shirts with our design as a function of the number of T-shirts. b. Your team has 35 members. If a T-shirt is purchased for ever member, what would be the cost? 13. Line is a reflection in the -ais of line k. Write an equation that represents line k. (0, ) (3, ) Copright Big Ideas Learning, LLC Algebra 1 117

7 Name Date.1 Enrichment and Etension Coordinate Geometr: Area of a Polgon How would ou find the area of a triangle when the figure has no sides parallel to either ais? Find the area of the triangle whose vertices are A 1, 0, B 3,, and C, 3. ( ) ( ) ( ) A method for finding area is to include the triangle in a rectangle, find the area of the right triangles formed, and subtract those areas from the total area of the rectangle A B Area of rectangle = 0 square units 3 C Area of triangle X = 1 = square units Area of triangle Y = =.5 square units Area of triangle Z = =.5 square units Area of ( ) ABC = = 0 11 = 9 square units In Eercises 1 5, find the area of the figure with the given vertices. 1. X(, ), Y( 1, 0 ), Z(, ) A X Z 1 C B Y. E( 0, 0 ), F(, 3 ), G( 5, ) 3. A(, 3 ), B( 8, 10 ), C(, ). J(, ), K(, ), L( 5, 0 ), M( 0, ) 5. P( 3, 0 ), Q(, ), R(, 3 ), S(, 1 ), T( 1, 3) 118 Algebra 1 Copright Big Ideas Learning, LLC

8 Name Date.1 Puzzle Time What Paces Back And Forth On The Ocean Floor? Write the letter of each answer in the bo containing the eercise number. Write an equation of the line with the given slope and -intercept. 1. slope: 3; -intercept: 8. slope: 3 ; -intercept: 9 3. slope: 1 ; -intercept: 0. slope: 5; -intercept: 7 8 Write an equation of the line that passes through the given points. 5. (, ), ( 0, 6) 6. (, 3 ), ( 0, 3) 7. ( 3, 0 ), ( 0, ) 8. ( 0, 11 ), ( 9, 7) 9. ( 8, 0.6 ), ( 0, 1.) Answers f K. ( ) 1 E. = + 5 = R. = + 3 S. = W. f 1 ( ) = 3 V. = 11 E. = 3 8 A. = 3 R. = 6 C. = Write a linear function f with the given values. 10. f ( ) f ( ) 0 = 7, 7 = f ( ) f ( ) 10 = 0, 0 = 5 O. = 1 f U. ( ) 8 = 7 7 = 1 = f( 1 ), f( 0) N. = The water park charges $15 for a birthda part. Guests cost $1 each. Write a linear model that represents the total cost of a birthda part as a function of the number of guests Copright Big Ideas Learning, LLC Algebra 1 119

9 . Start Thinking How can ou find a linear equation from a graph for which ou do not know the -intercept? Describe a situation in which ou might know the slope but not the -intercept. Provide a graph of this situation.. Warm Up Write an equation in slope-intercept form with the given slope and -intercept. 1. m = 3; b = 6. m = 3 ; b = 3. m = ; b =. m = 1 ; b = 5. m = 1; b = 5 6. m = ; b = 9. Cumulative Review Warm Up Solve the formula for the indicated variable. 1. Profit: P = R C; Solve for R.. Volume of a clinder: V = πr h; Solve for r. 3. Area of a trapezoid: A 1 hb ( b) = + ; Solve for h. 1. Average acceleration of an object: a v t v 1 = 0 ; Solve for t. 10 Algebra 1 Copright Big Ideas Learning, LLC

10 Name Date. Practice A In Eercises 1 3, write an equation in point-slope form of the line that passes through the given point and has the given slope. 1. ( 3, 1 ); m =. (, 7 ); m = 3 3. ( ), 3 ; m = 5 In Eercises and 5, write an equation in slope-intercept form of the line shown.. 5. (, ) ( 3, ) (5, 0) 1 (, 1) In Eercises 6 8, write an equation in slope-intercept form of the line that passes through the given points. 6. ( 6, 3 ), ( 3, 10 ) 7. ( 5, ), ( 15, ) 8. (, 3 ), (, 9) In Eercises 9 11, write a linear function f with the given values. 9. f() 1 = 3, f( 3) = 10. f( 6) = 9, f( 5) = f( ) f( ) 3 = 5, 3 = 5 In Eercises 1 and 13, tell whether the data in the table can be modeled b a linear equation. Eplain. If possible, write a linear equation that represents as a function of You are renting a paddle board. The compan charges a $50 fee and $0 per half-da. a. Write an equation that represents the total cost (in dollars) of renting a paddle board as a function of the number of half-das. b. Find the total cost of renting a paddle board for 7 half-das. Copright Big Ideas Learning, LLC Algebra 1 11

11 Name Date. Practice B In Eercises 1 3, write an equation in point-slope form of the line that passes through the given point and has the given slope. 1. (, 5 ); m = 1. ( 3, 1 ); m = 3. (, 6 1 ); m = In Eercises and 5, write an equation in slope-intercept form of the line shown ( 5, 3) (, 0) 8 (6, ) (9, 5) In Eercises 6 8, write an equation in slope-intercept form of the line that passes through the given points. 6. ( 3, 6 ), ( 5, 6) 7. (, ), ( 5, ) 8. ( 7, 18 ), ( 7, 1) In Eercises 9 11, write a linear function f with the given values. 9. f ( 5) =, f( 7) = 10. f( ) = 1, f ( 1) = f( ) f ( ) In Eercises 1 and 13, tell whether the data in the table can be modeled b a linear equation. Eplain. If possible, write a linear equation that represents as a function of. 8 = 1, 3 = The equation 5 ( 8) = + represents the cost (in dollars) of making our own juice (in fluid ounces). a. What is the slope of the line? Interpret the slope in the contet of this situation. b. Write the equation as a linear function. c. Use the linear function in part (b) to determine the base cost of making our own juice. 1 Algebra 1 Copright Big Ideas Learning, LLC

12 Name Date. Enrichment and Etension Challenge: Writing Point-Slope Form Point-slope form of a line is ver applicable in both algebra and geometr. It is ver simple to write point-slope form from a figure or line on a graph, but suppose ou had another form of an equation. How would ou rewrite it in point-slope form? Eample: If 1 = 1 3, write the point-slope form of the line given (ou must get 3 6 whole-number coordinates). 1 = ( 1 ) = ( ) = 18 = 5 18 = 5 18 Multipl each side b 6. Combine like terms. Because 18 is not divisible b 5, subtract from each side. = 5 0 ( ) = ( ) 1 5 Factor from the left side of the equation, and factor 5 from the right. 5 ( ) 1 = Divide b. In Eercises 1, write the linear equation in point-slope form. You must tr to get whole-number coordinates = = = 1. = Copright Big Ideas Learning, LLC Algebra 1 13

13 Name Date. Puzzle Time What Did The Wall Sa To The Bookcase? Write the letter of each answer in the bo containing the eercise number. Write an equation in point-slope form of the line that passes through the given point and has the given slope. 1. ( 5, 6 ), m =. ( 7, 0 1 ), m = 3. ( 1, ), m = 1. ( 3, 11 ), m = Write an equation in slope-intercept form of the line that passes through the given points. 5. ( 9, ), (, 11) 6. ( 8, 10 ), ( 1, 13 ) 7. ( 1, 15 ), ( 7, 15) 8. ( 6, 1 ), (, 16 ) Write a linear function f with the given values. 9. f() f() 3 = 3, = 10. f() f ( ) 3 = 9, = 11. f( ) f ( ) 10 =, 8 = 5 1. f( ) f ( ) 1 = 6, = You pa a registration fee and a monthl fee to join a local fitness center. The table shows the total cost of joining the fitness center for different numbers of months. Write an equation that represents the total cost (in dollars) of joining the fitness center as a function of the number of months. 9 8 Answers L. + = ( + 1) H. f( ) = Y. = E. 6 = ( 5) S. = 15 E. = F. 11 = ( + 3) 9 R. f( ) = + 6 H. f ( ) = P. f( ) = U. 0 = 1 ( + 7) 8 O. = 3 3 L. f( ) = 6 Months, Total cost (dollars), f() Algebra 1 Copright Big Ideas Learning, LLC

14 .3 Start Thinking Use our knowledge of slope to eplain how ou can determine if two lines are parallel b looking at their graphs. Graph the lines = 5 and = 5. Do the lines make 90 angles at the point of intersection? Does this prove or disprove the idea that perpendicular lines have opposite slopes?.3 Warm Up Write an equation in point-slope form of the line that passes through the given point and has the given slope. 5, 7 ; m = 3. (9, 3); m = 8 1. ( ) 3. ( 0, 1 ); m = 3. ( ) 3, 0 ; m = 1 5. (, ); m = 6. ( 5, 3 1 ); m = 7.3 Cumulative Review Warm Up Write the sentence as an inequalit. Graph the inequalit. 1. A number q is greater than 7 or less than 1.. A number p is greater than or equal to 6 and less than A number n is less than 6 1 and at least 11.. A number s is no more than 0. or greater than 10.. Copright Big Ideas Learning, LLC Algebra 1 15

15 Name Date.3 Practice A In Eercises 1 and, determine which of the lines, if an, are parallel. Eplain. 1. Line a passes through ( 1, 1 ) and ( 1, 3 ). Line b passes through ( ) ( ) Line c passes through ( ) ( ). Line a: = + 1 3, and 0,. Line b: = 5 0, 1 and 3, 3. Line c: + = In Eercises 3 and, write an equation of the line that passes through the given point and is parallel to the given line. 1, 3 ; 5 3. ( ) =. ( ), 1 ; = + 3 In Eercises 5 and 6, determine which of the lines, if an, are parallel or perpendicular. Eplain. 5. Line a passes through (, 3 ) and ( 1, 1 ). Line b passes through ( 3, 1 ) and ( 1, ). Line c passes through ( 0, ) and ( 3, ). 6. Line a: = + 7 Line b: = + Line c: + = 3 In Eercises 7 and 8, write an equation of the line that passes through the given point and is perpendicular to the given line. 7. (, 3 1 ); = ( ) 3 6, 1 ; = 5 5 In Eercises 9 and 10, write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line (, ) (, ) In Eercises 11 13, determine whether the statement is sometimes, alwas, or never true. Eplain our reasoning. 11. A line with a positive slope and a line with a negative slope are parallel. 1. A vertical line is perpendicular to the -ais. 13. Two lines with the same -intercept are perpendicular. 16 Algebra 1 Copright Big Ideas Learning, LLC

16 Name Date.3 Practice B In Eercises 1 and, determine which of the lines, if an, are parallel. Eplain. 1. Line a passes through ( 1, ) and ( 1, 5 ). Line b passes through (, 7 ) and ( 0, ). Line c passes through ( ) ( ). Line a: 6 = + 1 Line b: = , and, 5. Line c: 6 + = 5 In Eercises 3 and, write an equation of the line that passes through the given point and is parallel to the given line. 1, 3 ; 8 3. ( ) =. ( ) 3, 5 ; 3 = 1 In Eercises 5 and 6, determine which of the lines, if an, are parallel or perpendicular. Eplain. 5. Line a passes through ( 5, ) and ( 1, 1 ). Line b passes through ( 3, 5 ) and ( 3, 6 ). Line c passes through ( ) ( ) 6. Line a: + = 3 Line b: 6 = 3 1 0, 7 and 1, 1. Line c: 8 = 5 In Eercises 7 and 8, write an equation of the line that passes through the given point and is perpendicular to the given line. 7. ( 3, 1 ); = ( ) 8, 5 ; = + 3 In Eercises 9 and 10, write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line (6, 1) (, ) In Eercises 11 13, determine whether the statement is sometimes, alwas, or never true. Eplain our reasoning. 11. A line with a positive slope and a line with a negative slope are perpendicular. 1. A vertical line and a horizontal line are perpendicular. 13. Two horizontal lines are perpendicular. Copright Big Ideas Learning, LLC Algebra 1 17

17 Name Date.3 Enrichment and Etension Coordinate Geometr Proofs Recall that two lines are parallel if their slopes are equal, and two lines are perpendicular if their slopes are negative reciprocals. In geometr, we can prove that four-sided figures are certain quadrilaterals b using the following formulas and rules for each specific quadrilateral. Distance Formula: ( ) ( ) ( 1 + ) ( 1 + ) d = Midpoint Formula:, 1 Slope Formula: m = 1 Coordinate Proof Methods: Quadrilateral Prove the following Formulas needed Parallelogram Show that each pair of opposite sides are parallel. Slope Formula Rectangle 1. Show that opposite sides are parallel.. Show that adjacent sides are perpendicular. Slope Formula Rhombus Show that all sides are congruent. Distance Formula Square Trapezoid 1. Show that the figure is a parallelogram.. Show the figure is a rhombus. 1. Show that one pair of opposite sides is parallel.. Show that the other pair of sides is not parallel. Slope Formula Distance Formula Slope Formula In Eercises 1, graph the quadrilateral and prove it is either a parallelogram, rectangle, rhombus, square, or trapezoid. 1. J(, 3 ), K(, ), L( 6, ), M( 0, 3). A(, 0 ), B( 6, ), C( 9, ), D( 3, 5) 3. W( 6, 3 ), X(, 3 ), Y(, 1 ), Z( 0, 5). D( 3, 3, ) E( 0, 3, ) F( 0,, ) G( 3, ) 18 Algebra 1 Copright Big Ideas Learning, LLC

18 Name Date.3 Puzzle Time What Do Snowmen Wear On Their Heads? Write the letter of each answer in the bo containing the eercise number. Determine whether the lines are parallel, perpendicular, or neither. 1. Line a passes through (, 5 ) and ( 0, 1 ); Line b passes through ( ) ( ) 3, 1 and 1, 3. A. parallel B. perpendicular C. neither. Line a passes through ( 1, ) and ( 3, 6 ); Line b passes through ( ) ( ) 3, 6 and 1, 3. A. parallel B. perpendicular C. neither 3. Line a passes through (, 5 ) and (, 8 ); Line b passes through ( ) ( ) R. parallel S. perpendicular T. neither. line a: 5 = 9; line b: + 5 = 6 D. parallel E. perpendicular F. neither 5. line a: = 8 + 1; line b: 6 1 = I. parallel J. perpendicular K. neither 6. Write an equation of the line that passes through (, 6) 6, 7 and 3, 5. and is parallel to = 3 8. A. = 3 18 B. = 3 6 C. = Write an equation of the line that passes through ( ), 5 and is perpendicular to = 1 1. O. = + 3 P. = + 13 Q. = Copright Big Ideas Learning, LLC Algebra 1 19

19 . Start Thinking Sketch a coordinate plane, showing onl the first quadrant. Draw line q with an positive slope, horizontal line r, and line s with an negative slope. Describe what happens to the -values as the -values increase for each line. Give an eample of one real-life situation that represents each tpe of slope.. Warm Up Use the graph to write an equation of the line in slope-intercept form (, ) (3, 1) 8 (0, 3) (, 3) (0, 5) ( 3, 3) 8 (, 7) (1, 1). Cumulative Review Warm Up Graph the linear equation. Identif the -intercept. 1. = 5. = 3 3. =. 3 = Algebra 1 Copright Big Ideas Learning, LLC

20 Name Date. Practice A 1. The scatter plot shows students' scores for Quiz 1 and Quiz. Students Scores Quiz Quiz 1 a. What is the Quiz 1 score for a student who earned a score of 13 on Quiz? b. Did an student(s) earn the same score on both Quiz 1 and Quiz? Eplain. c. Does there appear to be a difference between the Quiz 1 scores and the Quiz scores? Eplain. In Eercises and 3, tell whether and show a positive, a negative, or no correlation The table shows the number of pineapple plants in a garden ears since a. Write an equation that models the approimate number of pineapple plants as a function of the number of ears since 00. b. Interpret the slope and -intercept of the line of fit. Copright Big Ideas Learning, LLC Algebra 1 131

21 Name Date. Practice B 1. The scatter plot shows the prior bowling averages of competitors at the bowling tournament and their highest scores during the tournament. Highest score Bowling Scores Bowling average a. How man competitors bowled above their average during the tournament? b. Did an bowler(s) bowl their average as their highest score? Eplain. c. What are the scores of the competitors with the greatest difference between their bowling average and their highest score? In Eercises and 3, tell whether and show a positive, a negative, or no correlation The table shows the total number of rolls of wrapping paper sold b a student after weeks a. Write an equation that models the number of rolls of wrapping paper as a function of the number of weeks. b. Interpret the slope and -intercept of the line of fit. 13 Algebra 1 Copright Big Ideas Learning, LLC

22 Name Date. Enrichment and Etension Correlation Coefficient In data analsis, there is a useful number called the correlation coefficient. This number gives a measure of how well a group of data is clustered around a line of best fit. If the data points are clustered closel around a line with positive slope, then the correlation coefficient r is close to 1. The value of r is close to 1 when the data points are clustered closel around a line with negative slope. If there is no close correlation, then the value of r is close to 0. r = 1 r = 1 r = 0 How to calculate the correlation coefficient: r = ( ) ( )( ) n ( ) ( ) n n In Eercises 1 and, use the formula to find the correlation coefficient for the set of data. 1. age of Labrador puppies vs. weight. hours studing vs. grade on eam Weeks Weight (pounds) Hours Grade Copright Big Ideas Learning, LLC Algebra 1 133

23 Name Date. Puzzle Time On What Da Do Spiders Eat The Most? Write the letter of each answer in the bo containing the eercise number. Using a scatter plot of the data, tell whether and show a positive, a negative, or no correlation. 1. ( 3, ), (, 0), ( 1, 1 ), ( 0, 0 ), ( 0, 1 ), ( 0, ), ( 1, ), (, 3) A. positive correlation B. negative correlation C. no correlation. (, 5, ) ( 1, 3, ) ( 1,, ) ( 0,, ) ( 0,, ) ( 1,, ) (, 1, ) ( 3, 0) X. positive correlation Y. negative correlation Z. no correlation 3. ( 3,.5 ), (, ), (, 3), ( 1, 3 ), ( 1, ), ( 0, 0 ), ( 0, 1 ), (, 1) K. positive correlation L. negative correlation M. no correlation. ( 3, 0, ) ( 3,, ) (, ), (,, ) ( 0, 0, ) ( 1, 3, ) (,, ) ( 3, ) B. positive correlation C. negative correlation D. no correlation 5. The table shows the dail ticket sales of the latest movie. Using a scatter plot of the data, write an equation that models ticket sales as a function of the number of das that the movie has been in theaters. Das, Sales (millions), E. = 0 F. = + 0 G. = The table shows the number of vehicles that were cleaned at the car wash hours since the car wash opened. Using a scatter plot of the data, write an equation that models the number of vehicles as a function of the number of hours since the car wash opened. Hours, Vehicles, W. = 1 X. = + 1 Y. = Algebra 1 Copright Big Ideas Learning, LLC

24 .5 Start Thinking Compare the scatter plots below. Which line best represents the data? Support our answer with evidence from the graphs Warm Up Plot the points from the table in a coordinate plane. Write the equation of the line in slope-intercept form Cumulative Review Warm Up Solve the equation. Determine whether the equation has one solution, no solution, or infinitel man solutions. 1. t 3 = 13 + t. 3h = 6h = 7( ). 5 ( g 5) = 35 ( g 10) ( m) = 9 ( 6m) 6. 3( t 5) = ( t) 5 Copright Big Ideas Learning, LLC Algebra 1 135

25 Name Date.5 Practice A In Eercises 1 and, use residuals to determine whether the model is a good fit for the data in the table. Eplain. 1. = = In Eercises 3 and, use a graphing calculator to find an equation of the line of best fit for the data. Identif and interpret the correlation coefficient The table shows the number of people in a room and the temperature in the room in degrees Fahrenheit, a. Use a graphing calculator to find an equation of the line of best fit. b. Identif and interpret the correlation coefficient. c. Interpret the slope and -intercept of the line of best fit. d. Approimate the temperature when 15 people are in the room. 136 Algebra 1 Copright Big Ideas Learning, LLC

26 Name Date.5 Practice B In Eercises 1 and, use residuals to determine whether the model is a good fit for the data in the table. Eplain. 1. = = In Eercises 3 and, use a graphing calculator to find an equation of the line of best fit for the data. Identif and interpret the correlation coefficient The table shows the average number of minutes per kilometer for runners and the total distance of a running race, (in kilometers) a. Use a graphing calculator to find an equation of the line of best fit. b. Identif and interpret the correlation coefficient. c. Interpret the slope and -intercept of the line of best fit. d. Approimate the average number of minutes per kilometer when the distance of a race is 31 kilometers. Copright Big Ideas Learning, LLC Algebra 1 137

27 Name Date.5 Enrichment and Etension Frequenc and Percentiles When test scores are reported, students are put into a certain percentile based on their grade compared to others who have taken the same test. The table shows certain test scores and their frequencies. The frequenc is the number of students who had a particular score. Eample: What score is in the 18th percentile? A score at the 18th percentile is the score that is just above the lowest 18% of scores. There are 50 scores, so the lowest 18% of the 50 total consists of 9 scores. The highest of these scores is a 55, so then the score at the 18th percentile would be also be a 55. Score Frequenc In Eercises 1 6, use the table above to find the score at the percentile. 1. 0th percentile. 50th percentile 3. 80th percentile. 58th percentile 5. 9nd percentile 6. 3th percentile In Eercises 7 9, use the table above to find the percentile at the score. 7. a score of 5 8. a score of a score of Algebra 1 Copright Big Ideas Learning, LLC

28 Name Date.5 Puzzle Time What Did The Mother Buffalo Sa To Her Son Before He Left? Write the letter of each answer in the bo containing the eercise number. Use a graphing calculator to determine whether the model is a good fit for the data in the table. 1. = O. es P. no. = I. es J. no 3. = M. es N. no Use a graphing calculator to find an equation of the line of best fit for the data Q. = R. = S. = A. =.95 + B. =.95 C. = Copright Big Ideas Learning, LLC Algebra 1 139

29 .6 Start Thinking Use a graphing calculator to graph the function f( ) = + 5. Use the TABLE function to make a list of five -values, beginning with = 5, separating each with a comma. Calculate how far apart each number is from the number before it. Compare this number to the function ou graphed, and eplain its significance..6 Warm Up Use the table to find the slope Cumulative Review Warm Up Tell which number ou would add to or subtract from each side of the inequalit to solve. 1. k 1 >. 0 b > 6. 7 m + 5. r > w > 8 10 Algebra 1 Copright Big Ideas Learning, LLC

30 Name Date.6 Practice A In Eercises 1 and, write the net three terms of the arithmetic sequence. 1. First term: 3. First term: 15 Common difference: 11 Common difference: In Eercises 3 6, find the common difference of the arithmetic sequence. 3. 9, 15, 1, 7,. 0, 10, 180, 150, 5. 15, 10, 5, 0, 6., 1, 1, 3, In Eercises 7 and 8, graph the arithmetic sequence. 7. 3, 10, 17,, 8., 6, 10, 1, In Eercises 9 and 10, determine whether the sequence is arithmetic. If so, find the common difference. 9. 1, 17, 1, 6, , 3,, 11, In Eercises 11 1, write an equation for the nth term of the arithmetic sequence. Then find a , 1, 1, 3, 1., 3, 8, 13, 13. 1, 6, 7 1, 9, 1.,, 6, 8, The first term of an arithmetic sequence is 6. The common difference of the sequence is two-thirds the first term. Write the net three terms of the sequence. 16. The height (in feet) of the water in a tank each hour after opening its drain can be estimated b the sequence in the table. Hours after opening drain 1 3 Height (feet) a. Write a function that represents the arithmetic sequence. b. Find and interpret the seventh term. c. Would the eighth term appl in this situation? Copright Big Ideas Learning, LLC Algebra 1 11

31 Name Date.6 Practice B In Eercises 1 and, write the net three terms of the arithmetic sequence. 1. First term: 8. First term: 0 Common difference: 5 Common difference: 1 In Eercises 3 6, find the common difference of the arithmetic sequence. 3., 1,, 5,.,, 6, 8, , 8., 8., 8.0, 6. 7 π, 5 π, 3 π, π, In Eercises 7 and 8, graph the arithmetic sequence. 7., 18, 3, 6, 8. 10, 7.5, 5,.5, In Eercises 9 and 10, determine whether the sequence is arithmetic. If so, find the common difference , 5, 37,, , 3, 8,, In Eercises 11 1, write an equation for the nth term of the arithmetic sequence. Then find a , 1, 7, 15, 1. 1,, 1, 11, , 180, 00, 0, 1. 7, 5, 1, 1, The first term of an arithmetic sequence is 3. The common difference of the sequence is 10 less than twice the first term. Write the net three terms of the sequence. 16. The volume (in cubic feet) of the water in a tank each hour after turning on a faucet can be estimated b the sequence in the table. Hours after turning on faucet 1 3 Volume (cubic feet) a. Write a function that represents the arithmetic sequence. b. The tank is in the shape of a rectangular bo. The length is 6 feet, the width is 3 feet, and the height is feet. Find the nth term that represents a full tank. Eplain. 1 Algebra 1 Copright Big Ideas Learning, LLC

32 Name Date.6 Enrichment and Etension Arithmetic Series An arithmetic series is the sum of a certain number of terms in a sequence. Let S stand for the following series, which starts with 5 and each consecutive term is 5 more than the previous term. S = Series formula: The series will sta the same when ou reverse the terms. After ou do this, add the two series together to obtain a final formula. So, the series formula is where n is the number of terms, first term, and is the last term. is the S = S = S = ( ) ( ) S = 6 35 S = 635 = 105 S = n ( a1 + an ) Eample: Find the sum 5 + ( ) ( ) ( ) a 8 1 = 5, an = 16, n = 8, so S = = 11 =. In Eercises 1 8, find the sum of the arithmetic series ( 1) ( + 3) + ( + 5) + ( 3 + 7) + ( + 9) + ( ) 7. odd whole numbers from 1 to even integers from 0 to 50 Copright Big Ideas Learning, LLC Algebra 1 13

33 Name Date.6 Puzzle Time What Do You Get When You Cross A Centipede With A Parrot? Write the letter of each answer in the bo containing the eercise number. Write the net three terms of the arithmetic sequence. 1. First term: ; Common difference: 9. First term: ; Common difference: , 11, 19, 7,. 3, 5, 7, 9, 5. 17, 8 1, 0, 8 1, 6. 5.,,.6, 1., Use an equation for the nth term of the arithmetic sequence to find a 1. 7.,, 6, 8, 8. 10, 9, 8, 7, , 5, 0, 5, 10. 7, 9, 11, 13, 11., 1,, 1, , 0.5, 0.75, 1.5, 13. The temperature of some water increases F ever hour after an initial temperature of 50 F. Use an equation for the nth term of the arithmetic sequence to find a6, the temperature of the water in F after 6 hours. Answers A. 1, 6, I. L. 9 A. 11, 13, 15 E L. K. 1 17, 5 1, 3 E. 13,, 31 A. 5 W. 5.5 T. 60 K. 0., 1.6, 3 I. 35,3, Algebra 1 Copright Big Ideas Learning, LLC

34 .7 Start Thinking Use work at a photo processing facilit. The price for processing 50 photos or fewer is $0.35 per photo. If a customer wants more than 50 photos, the cost is $18.00 plus $0.9 per photo. The situation described above can be thought of as two separate equations. Write a linear equation for each, specifing the domain..7 Warm Up Evaluate the function. 1. f( ) = 6 +, if = 3. g ( ) = 3+, if = 3 3. = + 5, if = 3. = 3, if = 5. f( ) = + 3, if = 3 6. g ( ) = 5+ 3, if = 5.7 Cumulative Review Warm Up Graph and compare the two functions. f = 3; g = 7 1. ( ) ( ) s = ; t = ( ) ( ) v = 3; w = ( ) ( ) c = 5 + ; d =. ( ) ( ) 3 Copright Big Ideas Learning, LLC Algebra 1 15

35 Name Date.7 Practice A In Eercises 1 6, evaluate the function. ( ) f + 3, if < 0 = 5, if 0 1. f ( ). ( ) f 5. 1 ( ). ( 0) f 3. f () 1 f 6. f ( 10) 7. On a trip, the total distance (in miles) ou travel in hours is represented b the piecewise function ( ) d 55, if 0 < 1.5 = 8.5, if 1.5 < ( ), if a. How far did ou travel in 1.5 hours? 3 hours?.5 hours? b. Write a real situation that could be represented b this piecewise function. In Eercises 8 11, graph the function. Describe the domain and range. 8. f( ), if < 3 = +, if 3 9. f ( ) 3,if 1 = 3, if > f( ) + 6, if < =, if 11. f( ) +, if < 0 =, if 0 In Eercises 1 and 13, write a piecewise function for the graph In Eercises 1 17, write the absolute value function as a piecewise function. 1. = = 16. = = 16 Algebra 1 Copright Big Ideas Learning, LLC

36 Name Date.7 Practice B In Eercises 1 6, evaluate the function. ( ) f +, if < 3 = 7, if 3 < 0 3 1, if 0 1. f ( 5). ( ) f 5. 1 ( ). ( 0) f 3. f () 1 f 6. f ( 3) 7. The total cost (in dollars) of ordering graduation announcements is represented b the piecewise function , if 0 < 5 c ( ) = , if 5 < , if 0 a. Determine the cost of ordering 5 announcements. Then determine the cost of ordering announcements. b. For what number of announcements less than 5 is it financiall better to purchase 5 announcements? c. For what number of announcements less than 0 is it financiall better to purchase 0 announcements? In Eercises 8 11, graph the function. Describe the domain and range. 8. f( ) + 5, if < 5 = 5, if 5 9. f( ) 3, if 1 = +, if > f( ) + 1, if < 3 =, if 3 < 0 3 +, if ( ) + 3, if < f =, if <, if In Eercises 1 15, write the absolute value function as a piecewise function. 1. = = + 1. = = Copright Big Ideas Learning, LLC Algebra 1 17

37 Name Date.7 Enrichment and Etension Greatest and Least Integer Functions For an real number, f ( ) For an real number, f ( ) Eample: = denotes the greatest integer less than or equal to. = denotes the least integer greater than or equal to. 0, if 0 1 ( ) = ; f =, if 1 < and ( ) f <, if < 3, if 0 < 1 f = =, if 1 < 6, if < f() = f() = In Eercises 1 6, graph and write an equivalent piecewise function. 1. f ( ) = + 3. f ( ) = f ( ) = f =. ( ) 1 5. f ( ) = 6. f( ) = Algebra 1 Copright Big Ideas Learning, LLC

38 Name Date.7 Puzzle Time What Do You Call A Nervous Zucchini? Write the letter of each answer in the bo containing the eercise number. Evaluate the function. ( ) f ( ) g 8, if < = 3 6, if + 5, if 3 = 7, if 3 < < 1 8, if 1 1. f ( ). f ( 6) 3. f ( 6). f ( 0) 5. f ( 3) 6. g ( 0) Answers E. 6 N. 1 E. 50 Y. 7 A. 15 I. 8 E. 18 G. 11 D G. 15 V. f( ) 3, if 0 = + 1, if > 0 7. g( 5) 8. g () 1 9. g ( ) 10. g( 3) G. f( ) + 1, if < 0 =, if 0 Write a piecewise function for the graph Copright Big Ideas Learning, LLC Algebra 1 19

39 Name Date Chapter Cumulative Review In Eercises 1 5, solve the equation and check our answer. 1. = 17. π + = 10π ( r 6) = 5. ( ) ( ) z = The cost to pla an online video game is either $16 if ou sign up for a ear or $18 per month. a. After how man months would the cost be the same? b. How man months would ou have to pla the game to make the earl subscription a better deal? In Eercises 7 9, solve the equation. Determine whether the equation has one solution, no solution, or infinitel man solutions = v 60 = 3( 0 5v) 9. 3( ) ( 3 1) In Eercises 10 13, solve the equation. Graph the solution(s), if possible. = 0 = = d = r 10 = = 1 In Eercises 1 and 15, write the sentence as an inequalit. 1. A number n is at least The number 13 is no more than a number h times. In Eercises 16 0, solve the inequalit. Graph the solution t > z + 11z < ( ) > and < 0. 5t or 6 + t 30 In Eercises 1 3, solve the inequalit. Graph the solution, if possible < 3. w <. At a visual graphics compan, the average starting salar for a new graphic designer is $37,000, but the actual salar could differ from the average b as much as $590. a. Write an absolute value inequalit to describe this situation. b. Solve the inequalit to find the range of starting salaries. 150 Algebra 1 Copright Big Ideas Learning, LLC

40 Name Date Chapter Cumulative Review (continued) In Eercises 5 8, determine whether the relation is a function. Eplain. 5. ( 1, 8, ) (, 8, ) ( 3, 8, ) (, 8, ) ( 5, 8 ) 6. ( 1, 7 ), ( 7, 3 ), ( 3, 5 ), ( 5, 1 ), ( 1, 3) In Eercises 9 31, find the domain and range of the relation and determine whether or not the graph represents a function The function = + 10 represents the amount of mone in our pigg bank (in dollars) after weeks. a. Identif the independent and dependent variables. b. Find the domain and range of the function. In Eercises 33 35, evaluate the function when = 3, 0, and. 33. f ( ) = g( ) = h ( ) = 5 6 In Eercises 36 38, graph the linear function. 36. f ( ) = 37. w ( ) = h ( ) 5 = f = + represents the distance in feet a snail is from a house 3 hours after it started crawling. 39. The function ( ) 1 a. What is the snail s distance from the house after 9 hours? b. How long will it take the snail to get 13 feet from the house? In Eercises 0, find the - and -intercepts of the graph of the linear equation. Use the intercepts to graph the linear equations. Label the intercepts = = = 11 Copright Big Ideas Learning, LLC Algebra 1 151

41 Name Date Chapter Cumulative Review (continued) In Eercises 3 5, find the slope and -intercept of the graph. Graph the linear equation. 3. = 3. = = 9 In Eercises 6 and 7, use the graphs of f and g to describe the transformation from the graph of f to the graph of g. 6. f ( ) = ; g( ) = 7. f ( ) = 5 + 1; g( ) = 5 + In Eercises 8 50, graph the function. Compare the graph to the graph of f =. Describe the domain and range. ( ) 8. t ( ) = 3 9. r ( ) = h 1 ( ) = 3 In Eercises 51 5, write an equation of the line with the given slope and -intercept. 51. slope: ; -intercept: 1 5. slope: 3 ; -intercept: slope: 1 ; -intercept: 5. slope: 3; -intercept: In Eercises 55 57, write an equation of the line in slope-intercept form (0, 3) (, 3) (0, ) (1, 3) (0, ) (, 1) In Eercises 58 61, write an equation in point-slope form of the line that passes through the given point and has the given slope. 58. ( 3, ); m = ( 7, 0 ); m = ( 3, 9 1 ); m = 61. ( 1, ); m = In Eercises 6 65, write an equation in point-slope form of the line that passes through the given points. 6. (, ), ( 5, 7 ) 63. (, ), ( 7, 8) 6. ( 5, 1 ), ( 3, 7) 65. ( 0, ), ( 3, ) 7 15 Algebra 1 Copright Big Ideas Learning, LLC

42 Name Date Chapter Cumulative Review (continued) In Eercises 66 68, write an equation of the line that passes through the given point and is parallel to the given line. 66. ( ) = 67. (, 0 ); = ( ), 3 ; 3 1 3, 7 ; + = 6 In Eercises 69 71, write an equation of the line that passes through the given point and is perpendicular to the given line. 69. ( ) = ( 1, 3 ); = 71. ( ) 0, ; 1, ; = 10 In Eercises 7 and 73, make a scatter plot of the data. Tell whether and show a positive, a negative, or no correlation In Eercises 7 76, graph the arithmetic sequence. 7., 0,, 8, 75. 3, 11, 19, 7, 76. 3, 9, 15, 1, In Eercises 77 79, determine whether the sequence is arithmetic. If so, find the common difference. 77.,, 7, 11, 16,, 78. 5, 1, 37, 3, 79. 7, 13, 19, 5, In Eercises 80 and 81, graph the function. Describe the domain and range , if 1 = 3 1, if < , if < = 1 3, if Copright Big Ideas Learning, LLC Algebra 1 153