The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m ?
-
A
-
B
-
C
-
D
Correct answer: A
Explanation
Choice A is correct. The line passes through the origin. Therefore, this is a relationship of the form , where k is a constant representing the slope of the graph. To find the value of k, choose a point
on the graph of the line other than the origin and substitute the values of m and d into the equation. For example, if the point
is chosen, then
, and
. Therefore, the equation of the line is
.
Choice B is incorrect and may result from calculating the slope of the line as the change in time over the change in distance traveled instead of the change in distance traveled over the change in time. Choices C and D are incorrect because each of these equations represents a line with a d-intercept of 2. However, the graph shows a line with a d-intercept of 0.
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