Question

the graph shows the amount of money miguel earns after working $x$ hours.

!amount earned vs. hours worked graph(graph with points (2,26) and (5,65))

what is the rate of change of the amount earned with respect to hours worked for this function?

• 13 dollars per hour
• 3 dollars per hour
• $\frac{1}{13}$ hours per dollar
• $\frac{2}{5}$ hours per dollar

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 given by \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Identify the two points

We have the points \((2, 26)\) and \((5, 65)\), so \(x_1 = 2\), \(y_1 = 26\), \(x_2 = 5\), \(y_2 = 65\).

Step3: Calculate the rate of change

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

Answer:

13 dollars per hour