Question

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.
step construction

number of steps	height (inches)
5	35
7	49
9	63
11	77

what is the rate of change of height off the ground with respect to the number of steps?
a 14 in. per step
b 1/7 in. per step
c 7 in. per step
d 1/14 in. per step

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let the number of steps be $x$ and the height be $y$.

Step2: Select two points

Let's take the points $(3,21)$ and $(5,35)$.

Step3: Calculate the rate of change

$m=\frac{35 - 21}{5 - 3}=\frac{14}{2}=7$.

Answer:

C. 7 in. per step