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 cost of the car wash.
find and describe the rate of change of the function.
the rate of change is. it represents the cost of?

number of gallons, x	total cost ($), y
3	22
6	34

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) formula for a linear function is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(x_1,y_1)=(0,10)$ and $(x_2,y_2)=(3,22)$.

Step2: Calculate rate of change

$m=\frac{22 - 10}{3-0}=\frac{12}{3}=4$.
The rate of change represents the cost per gallon of gas because as the number of gallons ($x$) increases, the total cost ($y$) increases at a rate that is the price per gallon.

Answer:

The rate of change is $4$. It represents the cost of one gallon of gas.