AP Pre-Calculus equation

[heresjonny]

Hello, this is the first time I have used a help site but I am tremendously puzzled by the following equation:

If it costs a company $32 to produce 5 items and $44 to produce 9 items, how much will it cost to produce 20 items, create a linear equation and then solve it.

Any help would be greatly appreciated Thank You

 

[Gene]

The general linear equation is
y=ax+b so you have
32=5a+b and
44=9a+b
Solve for a & b
Or you can recognize that a is the slope =(y₁-y₂)/(x₁-x₂)
a = (44-32)/(9-5)
then solve for the y intercept, b.