slope intercept form

Question

A car is worth $16,500 when it is three years old and $12,000 when it is six years old. Construct the equation in slope intercept form that represents the cost of a rental car.

I get the 2 points are 3, 16,500 and 6, 12,000 I am not sure how I would set up the equation in slope intercept form

Answer 1

Worth is a function of age/years...

Let x = age

Let y = worth

We have two points:  (3, 16500), (6, 12000)

 

y = mx + b is slope intercept form where m=slope, b=y intercept

 

We need the slope;

m = (12000-16500)/(6-3) = -4500/3 = -1500

 

The equation is of form:  y = -1500x + b

This makes sense because the worth is going down each year

so the line has a negative slope.

 

Use one of the given points as (x,y) and solve for b

 

12000 = -1500(6) + b

12000 = -9000 + b

b = 21000

 

Your equation is:  y = -1500x + 21000

Where y is the worth of the vehicle and x is the age in years

 

Note:  at age 0 years (new car) the vehicle is worth $21,000

At age 3 years:  y = -1500(3 ) + 21000 = $16,500

At age 6 years: y = -1500(6) + 21000 = $12,000