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

(x1, y1) and (x2, y2),

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