Graphical representation of an algebraic equation (lets say 2x + 2y = 2) can be established by considering the intercepts of both the variables involved in the mathematical equation.

An intercept is such a co-ordinate of a variable for which the corresponding co-ordinate of the other variable is zero. In other words, an intercept of a variable crosses through it's axis (x-intercept crosses through the x-axis and y-intercept crosses through the y-axis).

For the above hypothetical mathematical equation the x-intercept will be (1,0)

2x + 2(0) = 2

x = 1

and the y-intercept will be (0,1)

2(0) + 2y = 2

y = 1

Such technique can be used to find the solution set of two straight lines.

Consider the two straight lines be:

2x + 2y = 2

3x - 3y = 6

Now for our 2nd mathematical equation (3x - 3y = 6) the x and y intercepts will be (2,0) and (0,-2) respectively.

By drawing the above two mathematical equations on a graph, you can find the solution set of the two equations. That will be the point where the two equations intercept each other.