Example:

Here the Caterpillar will help you and Alice find your way through solving linear equations by graphing.

We must again start out with two equations.

4x-6y=12
2x+2y=6

There are two ways to solve these equations.  Here is what is called the slope-intercept way.  In order to do slope-intercept solve both equations for y.

4x-6y=12
subtract 4x from both sides and divide
both sides by -6.
y=2/3x-2.
2x+2y=6
subtract 2x from both sides and divide
both sides by 2.
y=-x+3.

Next decide what the slopes are and the y-intercepts of each equation.

The slope of y=2/3x-2 is 2/3 and the y-intercept is -2.
The slope of y=-x+3 is -1 and the y-intercept is 3.

Plot the y-intercepts and count the slope
(rise over run) in order to get the two lines.