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 22 gallons.

Answer 1

y = 1.7x + 2.75; $40.15

Explanation:

In order to solve the first part of the problem, you need to figure out the slope and y-intercept.

First, figure out the slope. The slope of a line is (change in y/change in x), so you can use any two pieces of data in the chart:

For example, (11, 21.45) and (15, 28.25)

The change in y is 28.25 - 21.45 = 6.8

The change in x is 15 - 11 = 4

So the change in y over change in x is:

6.8/4 = 1.7

And therefore, the slope is 1.7

Now, you have the slope of the equation, so you can start writing it out (m is the slope, b is the y-intercept):

y = mx + b where m = 1.7

y = 1.7x + b

Now, you need to find the y-intercept, or b. In order to do this, you just need to plug one of the given points into the equation and simplify:

For example, (17, 31.65)

31.65 = 1.7(17) + b

= 31.65 = 28.9 + b

= 2.75 = b

Therefore, the y-intercept is 2.75

So now you can write out the whole equation:

y = 1.7x + 2.75

For the second part of the problem, you need to figure out how much it costs to fill a 22-gallon tank. In this case, 22 is the x, so you are trying to solve for y by putting the x into the equation you just made:

y = 1.7(22) + 2.75

= y = 37.4 + 2.75

= y = 40.15

So it costs $40.15 for a 22-gallon tank to be filled