Question

Purchase a toyota 4runner for $25,635. Promised your daughter the SUV will be hers when the car is worth $10,000. The car dealer said the SUV will depreciate in value approximately $3,000 per year. Identify the m and b slope and the y intercept what each of them represents within the context of the problem.

Answer 1

y = -3000 + 25,635

m would be the slope, this will tell us how much the value changes over time.

m = -3000

b would tell us the initial value of the vehicle

b = 25,635

Explanation:

well if the inital value of the car is $25,635 this means that when

x = 0 y = 25,635

(0 , 25635)

this will be our first point

Now if you tell us that in 1 year depreciate in value $3,000

this means thaw when

x = 1 y = 25,635 - 3,000

x = 1 y = 22,635

(1, 22635)

Now that we have 2 points we can have the equation

First we take the slope as follows

y = mx + b

m = (y2 - y1) / (x2 - x1)

m = (22,635 - 25,635) / (1 - 0)

m = -3000 / 1

m = -3000

after calculating the slope we have to replace it in the following formula

(y - y1) = m (x - x1)

y - 25,635 = -3000 ( x - 0)

y - 25,635 = -3000x

y = -3000x + 25,635

b = 25,635

Finally we replace the value of y by 10000

10,000 = -3000x + 25,635

10,000 - 25,635 = -3000x

-15,635 = -3000x

-15,635/-3000 = x

5.21167 = x years

These are the years it would take for the value to be 10,000