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Algebra / Linear functions Difficulty: Medium

The figure presents the graph of a line in the coordinate plane. The horizontal m-axis is labeled “Time, in minutes,” and the numbers 0 through 7 are indicated. The vertical d-axis is labeled “Distance traveled, in feet,” and the numbers 0 through 7 are indicated. The line passes through the points with coordinates 1 comma 2 and 3 comma 6.

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 ?

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Explanation

Choice A is correct. The line passes through the origin. Therefore, this is a relationship of the form $d equals, k m$ , where k is a constant representing the slope of the graph. To find the value of k, choose a point $with coordinates m comma d$ 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 $with coordinates 2 comma 4$ is chosen, then $4 equals, k times 2$ , and $k equals 2$ . Therefore, the equation of the line is $d equals, 2 m$ .

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.