Question

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

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).
We have two points: \((2,26)\) and \((5,65)\).

Step2: Calculate the slope

Substitute into the formula: \(\frac{65 - 26}{5 - 2}=\frac{39}{3} = 13\).
The rate of change is 13 dollars per hour (since \(y\) is amount earned and \(x\) is hours worked, so dollars per hour).

Answer:

13 dollars per hour