Using SlopeIntercept Form for Graphing
In the slopeintercept form, a point on the line (the yintercept) and the
slope are readily available. To graph a line, we can start at the yintercept
and count off the rise and run to get a second point on the line.
Example 1
Using slope and yintercept to graph
Graph the line 2x  3y = 3.
Solution
First write the equation in slopeintercept form:
2x  3y 
= 3 
3y 
= 2x  3 
y 

The slope is
,
and the yintercept is (0, 1). Start at (0, 1) on the yaxis, then rise 2 and
run 3 to locate a second point on the line. Because there is only one line
containing any two given points, these two points determine the line. See the
figure below.
Methods for Graphing a Linear Equation
The three methods used for graphing linear equations are summarized as
follows.
Methods for Graphing a Linear Equation
1. Arbitrarily select some points that satisfy the equation, and draw a line
through them.
2. Find the x and yintercepts (provided that they are not the origin), and
draw a line through them.
3. Start at the yintercept and use the slope to locate a second point, then
draw a line through the two points.
