The graph shown models the number of candy bars a certain machine wraps with a label in x seconds. The

Question

The graph shown models the number of candy bars a certain machine wraps with a label in $x$ seconds.

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

Accepted Answer

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, x 1 , y 1 and x 2 , y 2 , on the line and the slope formula m = y 2 - y 1 x 2 - x 1 . The graph shown passes through the points 0 , 0 and 2 , 80 . Substituting these points for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = 80 - 0 2 - 0 , which is equivalent to m = 80 2 , 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.

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