the graph shows the amount of money miguel earns after working x hours. what is the rate of change of the…

the graph shows the amount of money miguel earns after working x hours. what is the rate of change of the amount earned with respect to hours worked for this function? amount earned vs. hours worked o $\frac{1}{13}$ hours per dollar o $\frac{2}{5}$ hours per dollar o 3 dollars per hour o 13 dollars per hour

the graph shows the amount of money miguel earns after working x hours. what is the rate of change of the amount earned with respect to hours worked for this function? amount earned vs. hours worked o $\frac{1}{13}$ hours per dollar o $\frac{2}{5}$ hours per dollar o 3 dollars per hour o 13 dollars per hour

Answer

Answer:

D. 13 dollars per hour

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a linear function $y = f(x)$ is given by $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Identify two points

We have the points $(2,26)$ and $(5,65)$ from the graph.

Step3: Calculate rate of change

$\frac{y_2 - y_1}{x_2 - x_1}=\frac{65 - 26}{5 - 2}=\frac{39}{3}=13$. The rate of change represents dollars per hour, so it is 13 dollars per hour.