? UNIT Stud Guide Review MDULE 313131313131313 ESSENTIAL QUESTIN Proportional Relationships How can ou use proportional relationships to solve real-world problems? EXAMPLE 1 Ke Vocabular constant of proportionalit (constante de proporcionalidad) proportional relationship (relación proporcional) slope (pendiente) Write an equation that represents the proportional relationship shown in the graph. Profit ($) 0 1 1 10 Bracelets sold Use the points on the graph to make a table. Bracelets sold 3 5 Profit ($) 9 1 15 1 Let represent the number of bracelets sold. Let represent the profit. The equation is = 3. Houghton Mifflin Harcourt Publishing Compan EXAMPLE Find the slope of the line. slope = rise run = 3 - = - 3 _ Run - - - Rise - Unit 13
EXERCISES 1. The table represents a proportional relationship. Write an equation that describes the relationship. Then graph the relationship represented b the data. (Lessons 3.1, 3.3, 3.) Time () 10 1 Distance () 3 5 Distance 1 Time Find the slope and the unit rate represented on each graph. (Lesson 3.). Words 3. Feet 10 Minutes 10 Seconds? MDULE ESSENTIAL QUESTIN Nonproportional Relationships How can ou use nonproportional relationships to solve real-world problems? EXAMPLE 1 Ke Vocabular linear equation (ecuación lineal) slope-intercept form of an equation (forma de pendiente-intersección) -intercept (intersección con el eje ) Jai is saving to bu his mother a birthda gift. Each week, he saves $5. He started with $5. The equation = 5 + 5 gives the total Jai has saved,, after weeks. Draw a graph of the equation. Then describe the relationship. Use the equation to make a table. Then, graph the ordered pairs from the table, and draw a line through the points. (weeks) 0 1 3 (savings in dollars) 5 30 35 0 5 The relationship is linear but nonproportional. Savings ($) 50 0 30 0 10 1 3 Time (wk) Houghton Mifflin Harcourt Publishing Compan 1 Unit
EXAMPLE Graph = - 1 -. The slope is -1, or - 1_. The -intercept is. 1 - -1-1 - Rise -3 1 -intercept Run EXERCISES Complete each table. Eplain whether the relationship between and is proportional or nonproportional and whether it is linear. (Lesson.1) 1. = 10. = - 3 0-3 0-1.5 -.5 3. Find the slope and -intercept for the linear relationship shown in the table. Graph the line. Is the relationship proportional or nonproportional? (Lessons.,.) - -1 0 1 - slope -intercept - - - - The relationship is. Houghton Mifflin Harcourt Publishing Compan. Tom s Tais charges a fied rate of $ per ride plus $0.50 per mile. Carla s Cabs does not charge a fied rate but charges $1.00 per mile. (Lessons.3) a. Write an equation that represents the cost of Tom s Tais. b. Write an equation that represents the cost of Carla s cabs. c. Steve calculated that for the distance he needs to travel, Tom s Tais will charge the same amount as Carla s Cabs. Graph both equations. How far is Steve going to travel and how much will he pa? Total cost ($) 10 10 Distance (mi) Unit 15
? MDULE 5 Writing Linear Equations ESSENTIAL QUESTIN How can ou use linear equations to solve real-world problems? Ke Vocabular bivariate data (datos bivariados) nonlinear relationship (relación no lineal) EXAMPLE 1 Jose is renting a backhoe for a construction job. The rental charge for a month is based on the number of das in the month and a set charge per month. In September, which has 30 das, Jose paid $700. In August, which has 31 das, he paid $715. Write an equation in slope-intercept form that represents this situation. ( 1, 1 ), (, ) (30, 700), (31, 715) m = - 1 - = 715-700 1 31-30 = 15 = m + b 715 = 15(31) + b 50 = b = 15 + 50 Write the information given as ordered pairs. Find the slope. Slope-intercept form Substitute for, m, and to find b. Solve for b. Write the equation. EXAMPLE Determine if the graph shown represents a linear or nonlinear relationship. 10 Points Rate of Change 10 The rates of change are not constant. The graph represents a nonlinear relationship. (0, 0) and (, 5) m = 5-0 - 0 = 5 _ (, 5) and (9, 7) m = 7-5 9 - = _ 3 (0, 0) and (9, 7) m = 7-0 9-0 = 7_ 9 Houghton Mifflin Harcourt Publishing Compan 1 Unit
EXERCISES 1. Ms. Thompson is grading math tests. She is giving everone that took the test a 10-point bonus. Each correct answer is worth 5 points. Write an equation in slope-intercept form that represents the scores on the tests. (Lesson 5.1) The table shows a pa scale based on ears of eperience. (Lessons 5.1, 5.) Eperience (ears), 0 Hourl pa ($), 9 1 19 9. Find the slope for this relationship. 3. Find the -intercept.. Write an equation in slope-intercept form that represents this relationship. 5. Graph the equation, and use it to predict the hourl pa of someone with 10 ears of eperience. 50 Hourl pa ($) 0 30 0 10 Does each of the following graphs represent a linear relationship? Wh or wh not? (Lesson 5.3) 10 Eperience (r). 7. Houghton Mifflin Harcourt Publishing Compan - - - - - - - - - - Unit 17
? MDULE Functions ESSENTIAL QUESTIN How can ou use functions to solve real-world problems? EXAMPLE 1 Ke Vocabular function (función) input (valor de entrada) linear function (función lineal) output (valor de salida) Determine whether each relationship is a function. A Input utput 3 10 5 0 5 The relationship is not a function, because an input,, is paired with different outputs, and 0. B 3 5 7 9 Since each input value is paired with onl one output value, the relationship is a function. EXAMPLE Sall and Louis are on a long-distance bike ride. Sall bikes at a stead rate of 1 miles per hour. The distance that Sall covers in hours is given b the equation = 1. Louis s speed can be found b using the numbers in the table. Who will travel farther in hours and b how much? Louis s Biking Speed Time (h), 3 5 7 Distance (mi), 0 100 10 Sall s ride: Louis s ride: = 1 = 0 = 1() = 0() = 7 = 0 Sall will ride 7 miles in hours. Louis will ride 0 miles in hours. Louis will go miles farther. Each distance in the table is 0 times each number of hours. Louis s speed is 0 miles per hour, and his distance covered is represented b = 0. Houghton Mifflin Harcourt Publishing Compan 1 Unit
EXERCISES Determine whether each relationship is a function. (Lesson.1) 1.. - - Input utput -1 0 1 1 Tell whether the function is linear or nonlinear. (Lesson.) 3. = 5 + 1. = + 3 5. Elaine has a choice of two health club memberships. The first membership option is to pa $500 now and then pa $150 per month. The second option is shown in the table. Elaine plans to go to the club for 1 months. Which option is cheaper? Eplain. (Lesson.3) Months, 1 3 Total paid ($), 15 30 5. Jenn rode her bike around her neighborhood. Use the graph to describe Jenn s bike ride. (Lesson.) Jenn's Ride Houghton Mifflin Harcourt Publishing Compan Speed (mi/h) Time (h) Unit 19
Unit Project.F.,.SP.1,.SP.,.SP.3 Mapping San Diego For this project, locate and draw a map of a small section of San Diego on a coordinate grid. Make Commercial Street our -ais. Make th Street our -ais. Mark the point (-, 0) at the intersection of Commercial Street and th Street. Mark the point (, 0) at the intersection of Commercial Street and 30 th Street. Use the scale determined b those points to determine the scale on the -ais. You ma make our map as detailed as ou wish, but to complete the project ou should find each of the following: The equation of 7 th Street The equation of L Street The equation of Franklin Avenue In each quadrant, the coordinates of at least two specific locations, such as a business, school, park or other landmark Use the space below to write down an questions ou have or important information from our teacher. MATH IN CAREERS ACTIVITY Cost Estimator A compan plans on selling MP3 plaers for $10. To make the MP3 plaers, a cost estimator determined it costs the compan $1500 per week for overhead and $5 for each MP3 plaer made. How much profit would the compan make if it sold 100 plaers in one week? Eplain. Houghton Mifflin Harcourt Publishing Compan 190 Unit