Question

the graph below represents magans earnings in dollars and cents, y, for working x hours. find the rate of change.

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 \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Identify two points

From the graph, we have two points: \((10, 165)\) and \((20, 330)\) (assuming the second point is \((20, 330)\) as the y - value at \(x = 20\) seems to be double of \(x = 10\) which is consistent with a linear relationship). Let \((x_1,y_1)=(10,165)\) and \((x_2,y_2)=(20,330)\).

Step3: Calculate the rate of change

Substitute the values into the slope formula:
\(m=\frac{330 - 165}{20 - 10}=\frac{165}{10}=16.5\)

Answer:

The rate of change is \(\$16.5\) per hour.