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# Using Slope-Intercept Form for Graphing

In the slope-intercept form, a point on the line (the y-intercept) and the slope are readily available. To graph a line, we can start at the y-intercept and count off the rise and run to get a second point on the line.

Example 1

Using slope and y-intercept to graph

Graph the line 2x - 3y = -3.

Solution

First write the equation in slope-intercept form:

 2x - 3y = -3 -3y = -2x - 3 y

The slope is , and the y-intercept is (0, 1). Start at (0, 1) on the y-axis, 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 y-intercepts (provided that they are not the origin), and draw a line through them.

3. Start at the y-intercept and use the slope to locate a second point, then draw a line through the two points.