Please Help Me solve this linear word problem

Question

There is a linear relationship between a car's weight and its gas mileage. An average car that weighs 2100 pounds gets 35 miles to the gallon, while a 3000-pound car gets 27 miles per gallon. If a car get 25 miles per gallon, how much should it weigh?

I know that the slope is negative but I struggled with the answer

Answer 1

Make 2 points where the x coordinate is weight and the y coordinate is the mpg:

Point 1 (2100,35) Point 2 (3000,27)

Because it is a linear relationship, you can set this up in the form y=mx+b where m is the slope and b is the y-intercept. You can solve for m by the change in y/change in x: m=(3000-2100)/(27-35)

m=(900)/(-8)

m=-112.5

We can solve for b by using either point. Let's use Point 1:

y=mx+b

35=(-112.5)(2100)+b

35=-236250+b

b=35+236+250

b=236285

So, now your equation is y=(-112.5)x + 236285 and we want to know what x is when y is 25:

25=(-112.5)x+236285

25-236285=-112.5x

-112.5x=-236260

x=-236260/-112.5

x=2100.09

Therefore, the weight of the car is about 2100.09 lbs.