There are several ways to graph linear equations.  One way is to create a table of values and plot and connect the points.  Another way is to put the linear equation in slope-intercept form, and use these values to plot.  A third way is to find the x- and y-intercepts of the line and plot and connect these two points.

To find the intercepts, we first solve the equation for y to put it into slope-intercept form.  The y-intercept is easy to find because it is the "b" in y = mx + b.

To find the x-intercept, we remember that the y-coordinate of an x-intercept is always 0.  So we set y = 0 in y = mx + b, and solve for x.  If we generically solve 0 = mx + b for x, we get x = -b/m.

We can also just simply substitute y = 0 into an equation to find the x-intercept, and x = 0 into an equation to find the y-intercept.

For example, if we want to find the intercepts of 2x + 7y = 28, we can do the following:

Find the x-intercept:  set y = 0

     2x + 7(0) = 28

     2x = 28

     x = 14

     The x-intercept is (14, 0)

Find the y-intercept:  set x = 0

     2(0) + 7y = 28

     7y = 28

     y = 4

     The y-intercept is (0, 4)

To graph the equation, we plot the intercepts (14, 0) and (0, 4) and connect them to form a line.

These class notes provide further explanation and examples.