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).

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
 
 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