We want to write a linear function that models the given situation, where a linear function is written as:
[tex]y = a*x +b[/tex]
where a is the slope and b is the y-intercept.
The function will be:
[tex]T(z) = (-0.02 gal/mi)*z + 13 gal.[/tex]
The information that we have here is:
The car gets 50 miles per gallon.
The tank holds 13 gallons of fuel.
We want to write a function that gives the number of gallons in the tank as a function of the miles driven.
Let's define the variable:
z = number of miles
Then the function T(z) will give us the number of gallons in the tank as a function of z.
[tex]T(z) = a*z + b[/tex]
We know that if there are no miles driven (z = 0), then the tank should be full, so we have:
[tex]T(0 mi) = 13 gal = a*0mi + b\\\\ 13 gal = b[/tex]
Then we found the value of b, and the function becomes
[tex]T(z) = a*z + 13 gal.[/tex]
Now we know that for every 50 miles driven, the car uses one gallon.
Then the rate (or slope) at which the fuel is consumed is:
[tex]a = -(1 gallon)/(50 miles) = -0.02 gal/mi[/tex]
Where the negative sign is because the fuel is being consumed.
We can replace that in the function to get:
[tex]T(z) = (-0.02 gal/mi)*z + 13 gal.[/tex]
If you want to learn more, you can read:
https://brainly.com/question/20286983
