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# Graphing Linear Equations

Objective Learn how to graph linear equations.

The main idea of this lesson is that you can draw the graph of a linear equation once you know two points on the graph, by simply placing a ruler along the two points. It is typically easy to find two points on a graph when it is in one of the standard forms.

Key Idea

If two points on a line are known, then the line can be drawn using a ruler.

Use a straightedge to draw the line going through the two points at (1, 2) and (4, -2).

How do we graph a line that is given to you in the form of an equation?

Find two points on the line.

## Graphing Lines in Slope-Intercept Form

Example 1

Graph y = 2 x + 3.

Solution

Two points are needed to graph this equation, which is given in slope-intercept form. Since the y-intercept is 3, one point is (0, 3). To find a second point, choose any other x value and compute the corresponding y value. For instance, choose x = 1.

 y = 2 x + 3 y = 2(1) + 3 Replace x with 1. y = 5

So the point at (1, 5) is also on the line. Now graph the line as shown on the figure below.

This works for all lines in slope-intercept form. The y-intercept is always given and another point can be generated by substituting any other value for x .

## Graphing Lines in Point-Slope Form

Example 2

Graph y - 4 = 3( x - 2).

Solution

One point on the line is easily found when an equation is in point-slope form. In this case, it is the point at (2, 4). To find a second point, choose an x value different from 2, say 4, and substitute it into the equation.

 y - 4 = 3( x - 2) y - 4 = 3(4 - 2) Replace x with 4. y - 4 = 3(2) y - 4 = 6 y = 10 Add 4 to each side.

So the point at (4, 10) is also on the line. Draw a line going through (2, 4) and (4, 10).

Equations in point-slope form can be graphed by first choosing the given point. Then generate a second point by substituting a different x value, and solving for y.