Plotting a Linear Equation On Graph

A linear equation in two variables has infinitely many solutions. We can plot these solutions on a graph. Each  solution represents a point on the graph, Let us take any three solutions  and plot them on the graph as P, Q and R, we will see that on joining these three points we get a straight line passing through them. We find that a linear equation in two variables is geometrically represented by a line such that:

(i)  Every solution of the linear equation represents a point on the line.

(ii) Every point on the line is a solution of the linear equation.

Illustration: Draw the graph of the equation y-x=2

Solution:  We will try to find three solutions for the linear equation,

When we have :

When we have :

When we have :

Thus, we have the following table exhibiting the abscissae and ordinates of points on the line represented by the given equation

Plotting the points (1,3), (3,5) and (4,6) on the graph paper and drawing a line joining them , we obtain the graph of the line represented by the given equation