Question

the graph below shows the amount of money a store earns for selling t - shirts.

t - shirt sales

what is the rate of change for the graph?

a. $10 per t - shirt
b. $2 per t - shirt
c. $40 per t - shirt
d. $20 per t - shirt

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) of a linear graph is given by $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in the y - value (money earned) and $\Delta x$ is the change in the x - value (number of T - shirts sold).

Step2: Choose two points from the graph

From the graph, we can take the points $(0,0)$ and $(4,40)$ (we could also take other points like $(8,80)$ etc.). Here, $\Delta x=4 - 0 = 4$ (change in number of T - shirts) and $\Delta y = 40-0=40$ (change in money earned).

Step3: Calculate the rate of change

Using the formula for rate of change (slope) $m=\frac{\Delta y}{\Delta x}$, we substitute $\Delta y = 40$ and $\Delta x = 4$. So $m=\frac{40}{4}=10$? Wait, no, wait. Wait, let's check another point. Let's take $(4,40)$ and $(8,80)$. Then $\Delta x=8 - 4=4$, $\Delta y=80 - 40 = 40$. Then $m=\frac{40}{4}=10$? Wait, no, wait the options have $10$ as option A. Wait, let's check the graph again. Wait, when $x = 4$ (number of T - shirts), $y = 40$ (money earned). So rate of change is $\frac{y}{x}=\frac{40}{4}=10$. So the rate of change is $\$10$ per T - shirt.

Answer:

A. $\$10$ per T - shirt