Question 103152
Intersection of any two equations (linear or not) is handled by setting the equations equal to each other. 
Here's an example. 
1. {{{y[1]=m[1]x+b[1]}}}
2. {{{y[2]=m[2]x+b[2]}}}
The intersection would be where {{{y[1]=y[2]}}}.
{{{y[1]=y[2]}}}
{{{m[1]x+b[1]=m[2]x+b[2]}}}
You can then proceed to solve for x.
{{{m[1]x-m[2]x+b[1]=m[2]x-m[2]x+b[2]}}}
{{{m[1]x-m[2]x+b[1]-b[1]=b[2]-b[1]}}}
{{{(m[1]-m[2])x=b[2]-b[1]}}}
{{{x[i]=(b[2]-b[1])/(m[1]-m[2])}}}
Once you have x, you can calculate y from (1) or (2) to get your intersection point. 
Here's an example
{{{y=2x+4}}}
{{{y=3x+5}}}
{{{x[i]=(5-(4))/(2-3)}}}
{{{x[i]=-1}}}
{{{y[i]=2(-1)+4}}}
{{{y[i]=2}}}
The intersection point for this example is (-1,2).
{{{ graph( 300, 300, -5, 5, -5, 5, 2x+4, 3x+5) }}}
Just as an interesting point, if the slopes of your lines were equal to each other, then your equation for {{{x[i]}}} would fail because of division by zero{{{m[1]-m[2]=0}}}. In that case, since the slopes are equal, the lines never meet because they are parallel.