Question

The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. The costs

of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the
function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck
whose tank size is 25 gallons.

Answer 1

Option (2)

Explanation:

Table given in the question shows the relation between the size of tank (x) and cost of gas to fill the tank f(x).

Since, relation is a linear function in the form of f(x) = mx + b

Graph of the function will be straight line.

Here 'm' = slope of the line

b = y-intercept

Since, two points (9, 23.55) and (15, 36.75) lie on this line.

Slope of the line =
`(y_2-y_1)/(x_2-x_1)`

=
`(36.75-23.55)/(15-9)`

=
`(13.2)/(6)`

= 2.2

By substituting the value of 'm' in the equation,

f(x) = 2.2x + b

Since, the given line passes through (9, 23.55),

23.55 = 2.2(9) + b

b = 23.55 - 19.8

b = 3.75

Equation of the function will be,

f(x) = 2.2x + 3.75

Cost to fill the tank and a car wash with size of the tank = 25 gallons,

f(25) = 2.2(25) + 3.75

= 55 + 3.75

= $58.75

Therefore, Option (2) will be the answer.