Graphing Linear Equations

The graph of a linear equation in two variables is a line (that's why they call it linear).

If you know an equation is linear, you can graph it by finding any two solutions

( x 1 , y 1 ) and ( x 2 , y 2 ) ,

plotting these two points, and drawing the line connecting them.


Graph the equation x+2y=7 .

You can find two solutions, corresponding to the x -intercepts and y -intercepts of the graph, by setting first x=0 and then y=0 .

When x=0 , we get:

0+2y=7 y=3.5

When y=0 , we get:

x+2( 0 )=7 x=7

So the two points are ( 0,3.5 ) and ( 7,0 ) .

Plot these two points and draw the line connecting them.

If the equation is in slope-intercept form or point-slope form, you can also use the slope to help you graph.


Graph the line y=3x+1 .

From the equation, we know that the y -intercept is 1 , the point ( 0,1 ) and the slope is 3 .  Graph the point ( 0,1 ) and from there go up 3 units and to the right 1 unit and graph a second point.  Draw the line that contains both points.

Horizontal and vertical lines have extra simple equations.


Horizontal line: y=3

Vertical line: x=2