Line segment A starts at (0, 80) and ends at (28000, 80). The equation is \(\displaystyle y=80\).

Line segment B starts at (28000, 80). It has a rise of -2, and a run of 1000; hence a slope of -1/500. This equation is \(\displaystyle y=\frac{-x}{500}+136\). This segment ends when y becomes negative.

The two lines resemble a hockey stick. Can these two equations be concatenated into one neat and tidy equation, and how would it be done?

As tkhunny says "not usually." However there are curve fitting techniques that might be useful, though often messy. The general approach that I've seen takes your two lines and links them together by fitting a conic section (usually a parabola) between the two lines. The problems come in:

1) You have to pick two arbitrary points on each line to fit your parabola

2) The parabola's major axis is at an angle to the +x axis making the equation for the parabola icky.

3) The parabola has to be tangent to the lines at the points you have chosen.

4) If you don't like the results after graphing you have to start all over again.

5) This method does not always work well.

6) This method is ridiculously time consuming.

7) When you are done you still don't have a single equation, just three equations you put together piece-wise.

Failing the parabola, circles and ellipses also work.

-Dan