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).

Question

Caleb Bolton

Mathematics

14 September, 01:45

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).

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Josiah Caldwell · 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