B Apply

Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.

26. The length of a bus route is 4 mi long on the sixth day and 4 mi long on the seventeenth day.
27. A babysitter earns $9 for 1 h and $36 for 4 h.
28. A student earns a 98 on a test for answering one question incorrectly and earns a 90 for answering five questions incorrectly.
29. The total cost, including shipping, for ordering five uniforms is $66. The total cost, including shipping, for ordering nine uniforms is $114.

State the independent variable and the dependent variable in each linear relationship. Then find the rate of change for each situation.

30. Snow is 0.02 m deep after 1 h and 0.06 m deep after 3 h.
31. The cost of tickets is $36 for three people and $84 for seven people.
32. A car is 200 km from its destination after 1 h and 80 km from its destination after 3 h.

Find the slope of the line that passes through each pair of points.

33. ( − 2 , negative 2 comma  1), (7, 1)
34. (4.25, 0), (3.5, 3)
35. ( − 1 2 , 4 7 ) , ( 8 , 4 7 ) open . negative , 1 half , comma , 4 sevenths . close . comma . open . 8 comma , 4 sevenths . close
36. ( − 5 , negative 5 comma  0.124), ( − 5 , − 0.584 ) open negative 5 comma negative , 0.584 , close
37. ( − 42.25 , negative , 42.25 , comma  5.2), (3.25, 3)
38. ( − 2 , 2 11 ) , ( − 2 , 7 13 ) open . negative 2 comma , 2 elevenths . close . comma . open . negative 2 comma , 7 thirteenths . close

39. Think About a Plan The graph shows the average growth rates for three different animals. Which animal's growth shows the fastest rate of change? The slowest rate of change?

    
    Image Long Description

    • How can you use the graph to find the rates of change?
    • Are your answers reasonable?
40. Open-Ended Find two points that lie on a line with slope − 9 . negative 9 .
41. Profit John's business made $4500 in January and $8600 in March. What is the rate of change in his profit for this time period?

Each pair of points lies on a line with the given slope. Find x or y.

42. ( 2 , 4 ) , ( x , 8 ) ;  slope = − 2 open 2 comma 4 close comma open x comma 8 close semicolon , slope , equals negative 2
43. ( 4 , 3 ) , ( 5 , y ) ;  slope = 3 open 4 comma 3 close comma open 5 comma y close semicolon , slope , equals 3
44. ( 2 , 4 ) , ( x , 8 ) ;  slope = − 1 2 open 2 comma 4 close comma open x comma 8 close semicolon , slope , equals negative , 1 half
45. ( 3 , y ) , ( 1 , 9 ) ;  slope = − 5 2 open 3 comma y close comma open 1 comma 9 close semicolon , slope , equals negative , 5 halves
46. ( − 4 , y ) , ( 2 , 4 y ) ;  slope = 6 open negative 4 comma y close comma open 2 comma 4 y close semicolon , slope , equals 6
47. (3, 5), (x, 2); undefined slope
48. Reasoning Is it true that a line with slope 1 always passes through the origin? Explain your reasoning.

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