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

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]

Step-by-step explanation:

step-by-step explanation:

step-by-step explanation: