Question

Mr. Shaw sells used cars. He earned $250 for selling 5 cars. Mr. Shaw earned $400 for selling 11 cars. Which of the following equations represents this situation, where c represents the number of cars Mr. Shaw sold and e represents the amount he earned?

a: e = 50c + 125
b: e = 25c + 125
c: e = 50c
d: e = 25c

Answer 1

b.
`e=25c+125`

Explanation:

We are told that Mr. Shaw earned $250 for selling 5 cars. Mr. Shaw earned $400 for selling 11 cars.

We can see that earnings of Mr. Shaw depends on selling of car, so selling of cars will be independent (x) and total earnings will be dependent (y).

Let us find slope of our line with given points (5,250) and (11,400)

`m=(y_2-y_1)/(x_2-x_1)`

`m=(400-250)/(11-5)`

`m=(150)/(6)=25`

This means that Mr. Shaw earns $25 for selling each car.

Now let us find equation of our line in slope intercept formula.

`y=mx+b`, where m= Slope and b= y- intercept.

Let us find b for our equation substituting coordinates of point (5,250) and m=25 in slope intercept form of equation.

`250=25*5+b`

`250=125+b`

`250-125=b`

`125=b`

`y=25x+125`

Now let e represent the amount earned by Mr. Shaw and c represent the number of cars sold.

So our equation will be:
`e=25c+125` and option b is the correct choice.