Question

Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $14,500 in 1982 and $65,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S

Answer 1

A linear function has the form : f(x)=ax+b

we are given that 

f(0)=a*0+b=b is $14,500.

so the sales in the first year were $14,500.

f(1) gives the sales in the second year     (year 83)
f(2) gives the sales in the third year          (year 84)
.
.
f(5) gives the sales in the sixths year        (year 87)


the slope of the line, a, is given by : 

$\frac{f(5)-f(0)}{5-0}= \frac{65,500-14,500}{5}= 10,200$

thus,

S=ax+b=10,200x+14,500


Answer: S=10,200x+14,500