28. 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 28 gallons.

Total cost (S)

Tank size (gal)

(x)

10

12

17

23.75

27.95

38.45

Answer: You're first asked to find the equation for the function in slope-intercept form. Slope-intercept means that you need to find an equation that can be written as y=mx+c, where m and c are numbers and m is the slope of the line and c is the y-intercept (i. e. the value of y when x is 0).

You already have three values of x and their corresponding y values (or f (x)).

If you write out your equation y=mx+c, subsituting in the values of x and y that you already know, you can then solve th equations as simultaneous equation to find your values of m and c.

So:

For x=10, y=21.75

so:

21.75=10m+c (Call this Equation 1)

For x=14, y=30.35

so:

30.35=14m+c (Call this Equation 2)

If you take Equation 2 from Equation 1, you will eliminate c leaving you with an equation you can solve to find the value of m. So:

[30.35=14m+c] - [21.75=10m+c]