Question

owen stops at a gas station. he pays for gas and a car wash. the table shows the total cost, y, as a function of the number of gallons of gas, x. the initial value is 10. it represents the car wash. find and describe the rate of change of the function. the rate of change is blank. it represents the cost of ?. number of gallons, x | total cost ($), y 0 | 10 3 | 22 6 | 34

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

Step2: Choose two points from the table

Take \((0, 10)\) and \((3, 22)\).

Step3: Calculate the rate of change

Substitute into the formula: \(\frac{22 - 10}{3 - 0}=\frac{12}{3} = 4\).
Check with another pair, say \((3, 22)\) and \((6, 34)\): \(\frac{34 - 22}{6 - 3}=\frac{12}{3}=4\). So the rate of change is 4, representing the cost per gallon of gas.

Answer:

The rate of change is \(\boldsymbol{4}\). It represents the cost of one gallon of gas.