You have already seen how to graph a linear equation by using a table (chart),
or by using the slope-intercept method .
Now, let's take a look at another graphing method.

 An Intercept Graphing Method:

Graph 2x + 3y = 12
Yes, you can re-write this equation and use a table or the slope-intercept method for graphing. But, there is another option which may be easier to use in this situation.

We are going to obtain the x-intercept and the
y-intercept. We will then choose one additional test point (to avoid possible errors) and show that all three points form a line.

 Remember: to find the y-intercept, set x = 0. to find the x-intercept, set y = 0.

If you want to organize your work,
you can set up a small table or chart.

 x y 0 0 ?

The first slot is for the
y
- intercept
(where x = 0).
The second slot is for the
x
- intercept
(where y = 0).
The third slot is for any test point you choose to plot to check for errors. (Hint: choose an x-value that will fit easily into the equation.)

 This graphing approach is particularly useful when your equation is in standard form, Ax + By = C.

Here is the completed chart
for the graph seen above.

 x y 0 4 6 0 3 2
y-intercept - set x = 0
2•0 + 3y = 12
3y = 12 and y = 4

x-intercept - set y = 0
2x + 3•0 = 12
2x = 12 and x = 6

We chose x = 3 to create the test point.
 2•3 + 3y = 12 6 + 3y = 12 3y = 6 y = 2 The fact that these three points form a straight line on the graph tells us that we did not make an error.

 Using the graphing calculator:

• We have seen the graphing calculator at work in graphing lines of the form y = mx + b.

• Since most graphing calculators require that equations be entered in "y=" form, they have a problem graphing vertical lines, such as x = 4. The third box listed below, will show you a trick to get your graphing calculator to deal with a vertical line without having to use the DRAW command.

• The graphing calculator can also create the equation of a line given two points on the line. The calculator uses a statistics feature called a "Linear Regression" to give you the slope and y-intercept of y = ax + b (the calculator's version of y = mx + b). Follow the link in the last box below to see how this works.