Help Please! Math equation 3 parts...?

Question

Bob Michaels purchased a house 8 years ago for $42,000. This year it was appraised at $67,500.

a. A linear equation V=mt+b, 0≤ t≤ 15, represents the value V of the house for 15 years after it was purchased. Determine m and b.

b. Write and solve an equation algebraically to determine how many years after purchase this house will be worth $74,000.

c. Determine how many years after purchase this house will be worth $80,250.

Answer 1

1. m is the slope, b is the y-intercept. If the x axis is years and y axis is cost, since he bought the house for $42000 and its been 0 years since he bought it when it was that price, one point on your graph will be (0, 42,000) after 8 years its $67500, so another point is (8, 67500)

use these 2 points to find the slope (m) and you get 25,500/8 which is 3187.5, so 3187.5 = m

since the first point crossed the x axis at 0, you know the y value of that coordinate is the y intercept, or b, so b= 42,000

2. V=mt + b, put m and b in and  you get your equation

V = 3187.5t + 42,000

3. Since V is the value, but 80, 250 in your equation for V

80250 = 3187.5t + 42000

-42000                  -42000

38250 = 3187.5t

/3187.5   /3187.5

12 = t

so 12 years

sorry its so wordy. i know math is usually just number and such but im bad at explaining most the time so i use a lot of words.. lol