Expert: Scott A Wilson - 10/19/2009

Question
As Hybrid car sales rise in the united states, automobile manufactures are expected to increase the number of available models in America. In 2006, 12 models were available. It is predicted that there will be 72 models in 2015.

Find a linear equation for the number of available models in terms of time t, where t represents the number of years since 200.

Answer
A linear equation since 2000 is to be found.

The two years gives are 2015 and 2006, and they have a difference of 2015 - 2006 = 9.
The difference is values is 72 - 12 = 60.
This would means that every year, there are 60/9 = 20/3 more models.

This says that the slope of the equation is 20/3.

Using the point-slope form of generating a line, { y-y0 = m(x-x0) } y - 6 = (20/3)(x-12).

This means we need to add 6 to both sides.  We will also multiply out the 20/3.  
This gives y = 20x/3 - 240/3 + 6.  Now -240/3 = -80, and -80 + 6 = -74,
so the final answer is y = 20x/3 - 74.