Question

Shortly after creating a car washing business, you made $65 washing ten

cars. Then after fifteen cars, you made $115. Build a model. Write an
explanation for the slope. Write an explanation for the y-intercept. How
many cars have you washed if you have made $255?

Answer 1

A) For the slope;

Rate of change in profit per change in number of cars washed = 10

B) when he had not washed any car, he was in debt of of $35

C) When he made $255, he had washed 29 cars

Explanation:

Slope intercept equation of a line is;

y = mx + c

you made $65 washing ten

cars. Thus, x = 10 and y = 65

So, 65 = 10m + c - - - - (eq 1)

Then after fifteen cars, you made $115.

Thus, x = 15 and y = 115

So; 115 = 15m + c - - - - (eq 2)

Subtract equation 1 from eq(2) to get;

115 - 65 = 15m - 10m + c - c

50 = 5m

m = 50/5

m = 10

Putting 10 for m in eq 1 gives;

65 = 10(10) + c

65 = 100 + c

c = 65 - 100

c = -35

A) Since the slope is m = 10 and slope is m = Δy/Δx, it means that;

Rate of change in profit per change in number of cars washed = 10

B) c = -35 is the y-intercept.

This means when x = 0, y = - 35.

It implies that when he had not washed any car, he was in debt of of $35

C) since we have the slope and intercept, equation is;

y = 10x - 35

If he has made $255,then we have;

255 = 10x - 35

255 + 35 = 10x

290 = 10x

x = 290/10

x = 29 cars washed.