Question

the graph below represents the number of miles, y, that janelys can drive her car for every x gallons of gas. find the rate of change.
janelyss gas mileage
(20,704)
(10,352)
miles driven
gallons of gas

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

From the graph, we have two points: \((10, 352)\) and \((20, 704)\). Let \((x_1, y_1)=(10, 352)\) and \((x_2, y_2)=(20, 704)\).

Step3: Calculate the rate of change

Substitute the values into the slope formula: \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{704 - 352}{20 - 10}=\frac{352}{10} = 35.2\).

Answer:

The rate of change is \(35.2\) miles per gallon.