A construction worker built steps up to a home. The table shows the linear relationship between the height off the ground in inches and the number of steps.
Number of Steps
3
5
7
9
11
Height (inches)
20
36
52
68
84
What is the rate of change of height off the ground with respect to the number of steps?
8 in. per step
16 in. per step
1/8 in. per step
1/16 in. per step
To find the rate of change of height off the ground with respect to the number of steps, we need to calculate the slope of the linear relationship between the height and the number of steps.
The slope is calculated by dividing the change in height by the change in the number of steps.
Change in height = (Height at the end - Height at the beginning) = (84 - 20) = 64 inches
Change in number of steps = (Number of steps at the end - Number of steps at the beginning) = (11 - 3) = 8 steps
Slope = Change in height / Change in number of steps = 64 inches / 8 steps = 8 inches per step
Therefore, the rate of change of height off the ground with respect to the number of steps is 8 inches per step. Therefore, the correct answer is:
8 in. per step