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.
