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 SlopeIntercept Form
Example 1
Graph y = 2 x + 3.
Solution
Two points are needed to graph this equation, which is given
in slopeintercept form. Since the yintercept 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 slopeintercept form. The
yintercept is always given and another point can be generated by
substituting any other value for x .
Graphing Lines in PointSlope Form
Example 2
Graph y  4 = 3( x  2).
Solution
One point on the line is easily found when an equation is in
pointslope 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 pointslope 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.
