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 Height (inches)
3 20
5 36
7 52
9 68
11 84
What is the rate of change of height off the ground with respect to the number of steps?
To find the rate of change of height off the ground with respect to the number of steps, we can look at the change in height divided by the change in the number of steps.
Between the first two points, the change in height is 36 - 20 = 16 inches, and the change in the number of steps is 5 - 3 = 2 steps.
So the rate of change is 16 inches / 2 steps = 8 inches per step.
We can also calculate the rate of change for the other pairs of points to confirm that it is consistent. The rate of change between the second and third points is 16 inches / 2 steps = 8 inches per step.
Similarly, the rate of change between the third and fourth points is 16 inches / 2 steps = 8 inches per step.
And the rate of change between the fourth and fifth points is 16 inches / 2 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.