Question

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

The equation for the function is f(x) = 1.90x + 3.50, and the cost of a fill-up and a car wash for a customer with a truck whose tank size is 25 gallons is $51 (option D).

How to find the function?

Find the Slope (m):

m = change in y / change in x =
`(26.30 - 18.70)/(12 - 8)`

m = 7.6/4

m = 1.90

Find the Y-Intercept (b):

Use one of the points (let's use the point (8, 18.70)):

18.70 = 1.9 * 8 + b

b = 18.70 - 15.2

b = 3.50

Write the Equation in Slope-Intercept Form:

f(x) = 1.90x + 3.50

Find the Cost for a Truck with a 25-Gallon Tank:

f(25) = 1.90 * 25 + 3.50

f(25) = 47.50 + 3.50

f(25) = 51.00

The answer is: Option D. f(x) = 1.90x + 3.50; cost for truck = $51.00.