Question the-gr

1.1 Linear Functions - Rate of change applications
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The graph shown models the number of candy bars a certain machine wraps with a label in x seconds.

  • The line slants sharply up from left to right.
  • The line passes through the following points:
    • (0 comma 0)
    • (2 comma 80)
    • (4 comma 160)
    • (6 comma 240)

According to the graph, what is the estimated number of candy bars the machine wraps with a label per second?

A.

2

B.

40

C.

78

D.

80

The graph shown models the number of candy bars a certain machine wraps with a label

Easy-difficulty · SAT Math · Linear Functions — Rate of change applications. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice B is correct. For the graph shown, the x-axis represents time, in seconds, and the y-axis represents the number of candy bars wrapped. The slope of a line in the xy-plane is the change in y for each 1 -unit increase in x . It follows that the slope of the graph shown represents the estimated number of candy bars the machine wraps with a label per second. The slope, m , of a line in the xy-plane can be found using any two points, x1,y1 and x2,y2, on the line and the slope formula m=y2-y1x2-x1. The graph shown passes through the points 0,0 and 2,80. Substituting these points for x1,y1 and x2,y2, respectively, in the slope formula yields m=80-02-0, which is equivalent to m=802, or m = 40 . Therefore, the estimated number of candy bars the machine wraps with a label per second is 40 .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.