Question

Janey bought a used bicycle for $640. the bike was 3 years old when she bought it, and cost $850 new. assuming it decreases in value by the same amount each year, write a linear equation for the value of the bicycle, v, when it is t years old (so t = 0 was when it was new).

Answer 1

The first thing we must do in this case is to define the variables.
We have then:
v: the value of the bicycle
t: years
The standard equation of the line is:
v-vo = m (t-to)
The slope is:
m = (v2-v1) / (t2-t1)
Substituting values:
m = (640-850) / (3-0)
m = -70
We choose an ordered pair:
(to, vo) = (0, 850)
Substituting values:
v-850 = -70 (t-0)
Rewriting:
v = -70t + 850
Answer:
assuming it decreases in value by the same amount each year, a linear equation for the value of the bicycle, v, when it is t years old is:
v = -70t + 850