Answers. Chapter 4 A15

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1 . =. Sample answer:. a. B is congruent to itself. A and D have the same line of sight, and so the are congruent. Because two angles are congruent, the third angles are congruent. Because the triangles have the same angle measures, the are similar. b. ; ;. ft; = = =. +. =. ft; The height of the flag pole is. feet.. a. B and E are right angles, and thus congruent. BCA and ECD are vertical angles, and so the are congruent. Because two angles are congruent, the third angles are congruent. Because the triangles have the same angle measures, the are similar. b.. =. ;. =.; =. mi.. Enrichment and Etension. es; The pattern repeats across the entire plane with no gaps or overlap. or. Sample answer:. triangles and heagons... Check students work.. triangle, triangle, triangle, triangle, heagon.. Sample answer: floor tiles, quilts 9. Sampler answer: rectangles. Puzzle Time SEA WEED Technolog Connection. Sample answer: Chapter. Start Thinking! For use before Activit. A and C; the graphs are lines.. Warm Up For use before Activit Copright Big Ideas Learning, LLC A

2 . Start Thinking!. For use before Lesson.. will var. Sample answers are given. =.... O For use before Lesson.. Warm Up. will var. Check students graphs... = + 9. a. Cost of Bananas Cost (dollars) A different solution point on the line is (, ). Pounds b. Sample answer: about $. c. $. O A different solution point on the line is (, ).. Sample answers are given. = +. (, ) School Lunch Account. a. =. Balance in account (dollars). (, ). Practice A =. = +. = + 9 School das b. school das A Copright Big Ideas Learning, LLC

3 . Practice B a.. Cost of meal (dollars) b. Sample answer: about $ c. $. = 9. = +. a. = + Coconuts under tree Beverages Famil Meal b. after weeks Copright Big Ideas Learning, LLC Falling Coconuts Weeks. not a line. Enrichment and Etension... Sum of First n Positive Integers Sum s n Integers. = +. = ; The graph of the quadratic equation is shaped like a U.. = + ; The graph of the absolute value equation is shaped like an upside-down V, or mountain peak.. Sample answer: The all have different shapes.. The -intercept would change and the graph would shift up or down. A

4 . Puzzle Time A CREAM PUFFIN. Start Thinking! For use before Activit. Sample answer: A ski slope is a natural incline, usuall a mountain or hill. The mathematical term slope refers to how steep an incline is.. Warm Up For use before Activit..... Start Thinking!. For use before Lesson. Monitor students during activit.. Warm Up For use before Lesson.... The lines are parallel.. The lines are parallel.. Practice A. a. lines A and C b. line B c. lines A and C; Both have a slope of.. The lines are parallel.. The lines are parallel. (, ) (, ). slope =. slope =. slope =. slope =. slope = (, ) (, ). Practice B. slope =. slope =. slope =.. slope = slope =. slope =. feet. a. slope =. b. The phone calls cost $. per minute. c. $. d. minutes. Enrichment and Etension. O. Sample answer: es; The opposite sides appear to have the same slope. It looks like the pairs of opposite sides are slanted the same wa.. From the top, going clockwise around the octagon, the slopes are,, undefined,,,, undefined, and. Sample answer: es; The predictions were correct.. es; The opposite sides have the same slope, so opposite sides are parallel.. Sample answer: es; There are three sets of line segments that look like the have the same slope the horizontal segments, the segments slanted up to the right, and the segments slanted up to the left.. From the top, going clockwise around the shape, the slopes are,,,,,,,,,,, and. Sample answer: es; The predictions were correct.. no; None of the segments are perpendicular because,, and. A Copright Big Ideas Learning, LLC

5 . Puzzle Time I M ON A ROLL Etension. Start Thinking! For use before Etension.. no; Both lines are horizontal and have a slope of.. es; Line = is vertical. Line = is horizontal. A vertical line is perpendicular to a horizontal line. The two lines do not appear to intersect. The graphs appear to intersect at right angles.. no; Adjacent sides are not perpendicular.. Start Thinking! For use before Activit. Sample answer: O Etension. Warm Up For use before Etension.. slope of line B: ; slope of line G:. slope of line B: ; slope of line G: Copright Big Ideas Learning, LLC Etension. Practice. A and B; The both have a slope of.. A and C; The both have a slope of.. no; = has an undefined slope and = has a slope of.. es; Both lines are vertical and have an undefined slope.. es; Both lines are horizontal and have a slope of.. es; Opposite sides have the same slope.. B and C; Line B has a slope of. Line C has a slope of. The product of their slopes is =.. A and C; Line A has a slope of. Line C has a slope of. The product of their slopes is ( ). = 9. es; Line = is vertical. Line = is horizontal. A vertical line is perpendicular to a horizontal line.. Warm Up For use before Activit.. =. =. =. =. =. =. Start Thinking! For use before Lesson. Check student s sketches; The line that passes through the origin will have an equation of the form = m.. Warm Up For use before Lesson.. no; The graph of the equation does not pass through the origin.. es; = ; The graph is a line that passes through the origin.. es; = ; The rate of change in the table is constant.. no; The rate of change in the table is not constant.. Practice A. es; = ; The graph is a line that passes through the origin.. no; The graph does not pass through the origin.. no; The rate of change in the table is not constant.. es; = ; The rate of change in the table is constant. A9

6 . a. Your friend runs. miles in hour. b. Sample answer: min. a. hamburgers; Sample answer: Hamburgers sell at a rate of about. per minute and wraps sell at a rate of. per minute. b. Miles Number sold Sample answer: The graph of the hamburgers sold is steeper. Hamburgers are selling at a faster rate than wraps.. Practice B. no; The graph does not pass through the origin.. es; = ; The graph is a line that passes through the origin.. es; = ; The rate of change in the table is constant.. es; = ; The rate of change in the table is constant.. a. = 9 b. It costs $9 to rent the lane for hour. c. $. a. es; The graph is a line that passes through the origin. b. = ; The height of the water in the tank rises inch per gallon of water. c.. in. Hours Hamburgers Sold Wraps Sold 9 Minutes. Enrichment and Etension. a. decrease b. increase c. It equals.. No, it does not have a constant rate of change.. direct variation. inverse variation. neither. neither. direct variation. inverse variation 9. inverse variation; c = n. direct variation; p = r. Puzzle Time CHEERIOS. Start Thinking! For use before Activit. Sample answer: The point (, 9) means that about 9 people attended the book fair on the th da. The graph is approimatel linear. The approimate slope is.. So, the book fair attendance increased b about. people each da.. Warm Up For use before Activit.... Start Thinking! For use before Lesson. Sample answer: You bu pairs of socks for $. each and pa $ for shipping. The slope is $. per pair and the -intercept is $. O O A Copright Big Ideas Learning, LLC

7 . Warm Up For use before Lesson.. B; slope =, -intercept =. A; slope =, -intercept =. C; slope =, -intercept =. a. Fertilizer (cups).... Fertilizing Grass Grass (square feet). Practice A. C ; ;. A ; ;. B ; ;. m = ; b =. m = ; b =. m = ; b =. m =.; b =. m = ; b = 9.. a. m = ; b = 9 Value (dollars) Value of a Car,,,, 9,,, Years b. The value of the car decreases $ per ear. c. $, is the initial cost of the car. d. The value of the car is $ after ears..... b. cup of fertilizer is needed per square foot of grass.. Practice B. m = ; b =. m =.; b =... m = ; b =. m =.; b =. m = ; b = a. =. + b. Cost (dollars) Downloading Music Songs per month m = ; b =.... c. $. Copright Big Ideas Learning, LLC A

8 . a. = b. Revenue (dollars) Pies and Pie Fillings Items sold c. items per month d. items per week. Enrichment and Etension Warm Up For use before Lesson.. Let represent non-highwa hours and let represent highwa hours; = + 9. Let represent number of hats and let represent number of T-shirts; = +. Puzzle Time THE LADY WHO GOT STOPPED FOR SPEEDING SO MANY TIMES THE POLICE GAVE HER SEASON TICKETS O. Start Thinking! For use before Activit. + = ; Sample answer: The graphs are the same. Multipling the original equation b and then adding to each side ields + =.. Practice A. = +. =. Warm Up For use before Activit.. = +. = +. = +. = +... = +.. Start Thinking! For use before Lesson. = + Sample answer: It is easier to write in standard form because of the information ou are given. You know that the sum of the two costs is $, or + =.. ;. ;.. (, ) (, ) (, ) (, ) 9. a. ; oranges and apples contain grams of fiber. b. ; apples and oranges contain grams of fiber. c. g d. g e. no; There cannot be. oranges in the package. A Copright Big Ideas Learning, LLC

9 . a. + = b. ;. a. = + b..; c. Jobs c. Electrician s Fees d.. h. Practice B. Hours worked as hair washer 9 9 Hours worked as host = +. =... ;. no -intercept;.. 9. a. + = b. ; c. d. das Snowboard das (, ) (, ) Ski Vacation (, ) (, ) Lift ticket das (, ) (, ) d. no; The visit cannot last a negative number of hours.. Enrichment and Etension. no; The graph is not a straight line... The trapeze artist starts feet right of center... The trapeze artist swings back and forth past center more than once.. seconds. feet. no; The peaks and valles on the graph do not var. Realisticall, the trapeze artist would not alwas swing to the same horizontal position. 9. no; It does not make sense to include negative numbers for time in this situation.. Puzzle Time THEY JUMP SHIP. Start Thinking! For use before Activit. The graph shows the temperature of an oven while it is preheating. The -intercept,, represents the temperature of the stove before it was turned on. The slope, degrees per minute, represents the heating rate.. Warm Up For use before Activit.. Total fee (dollars) Length of job (hours).. Start Thinking! For use before Lesson. = + ; the slope represents the monthl cost; the -intercept represents the enrollment fee. Copright Big Ideas Learning, LLC A

10 . Warm Up For use before Lesson.. =, = +, = +, =. = +, =, = +, = +. Practice A. = +, =, =, =. = +. = +. a.. inches per ear b. =. + c.. inches.. a. = +. = Number of pages Tping Speed (, ) (, ) Time (minutes). = +. = b. page or page per minute minutes. = + c. =. a. b. There are inches of water at seconds. There are inches of water after seconds. c. Inches of water Inches of water Filling a Bucket (, ) (, ) Time (seconds) Filling a Bucket (, ) (, ) Time (seconds). Enrichment and Etension The equations match up with the graph in the corresponding position.. Puzzle Time MORE THAN THE LION. Start Thinking! For use before Activit. Sample answer: es; You can plot the point and use the slope to graph the line. From the graph, ou can write the equation.. Warm Up For use before Activit... O O d. The inches of water in the bucket after seconds. e. =... Practice B. =, =, =, =. =. = + O O A Copright Big Ideas Learning, LLC

11 ... Start Thinking! For use before Lesson. Sample answer: If ou need to write the equation of a line given the slope and a point on the line, ou can find the -intercept (either graphicall or algebraicall). Then ou follow the steps for writing an equation given the slope and -intercept.. Warm Up For use before Lesson.. =. = +. =.. Practice A. = +. = = +. + = ( ). = ( + ). = ( ). + = ( + ). =. = + 9. =. = +. a. V = + 9 b. $9 c. $. Practice B. =. = +. = ( + ). + = ( ). + = ( + ). = ( + ). =. 9. O = = +. =. a. = + b. feet c. after seconds. Enrichment and Etension. The slope is the negative of the grade, written as a fraction or decimal.. Bunn Slope:, Medium Trail: Epert Trail:. = +,. ; The starting height of the trail is meters.. ; The length of the trail is meters.. = +.. no; It has a grade of %.. Puzzle Time THE TEAM SPIRIT Technolog Connection... a.. = + b. The sign changed. c. Sample answer: Visualize the points and determine whether the slope should be positive or negative to check our answer.. a.. b. The are reciprocals. c. Sample answer: Compare the change in to the change in to determine whether the slope is steeper (magnitude greater than ) or shallower (magnitude less than ) to check our answer Chapter. Start Thinking! For use before Activit. The onl solution is (, ). Methods ma var. Sample answer: Trial and error, to find two numbers where one number is greater than the other and whose sum is. Other methods are substitution and graphing. Copright Big Ideas Learning, LLC A

Chapter 4 ( 2, 2 ). Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 141) = = = = 15. The solution checks.

Chapter 4 ( 2, 2 ). Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 141) = = = = 15. The solution checks. Chapter Chapter Opener Tr It Yourself (p. ). ab = ( ) = ( ) = = = =. a b = ( ). a b = = = = + = + = + 9 =, or. a ( b a ). Point Q is on the -ais, units up from the origin. So, the -coordinate is, and the