Graph Linear Equations
How do we graph linear equations?
In the last section, we looked at how to
solve for the slope of an equation and how
to solve for the y-intercept.
Now we are going to look at how to graph
these lines
Remember….
To solve for the slope, we use the formula
y2  y1
m
x2  x1
Once we solve for the slope, we can use
that and a point to solve for the y-intercept
using the slope intercept form
y  m x b
Let’s try a few reminder problems
 (3,4) and (-2,3)
3 4
1 1
m


23 5 5
y  m x b
1
4  (3)  b
5
3
4  b
5
17
b
5
1
17
y  x
5
5
 (7,4) and (4,3)
3 4 1
m

47 3
y  m x b
1
3  ( 4)  b
3
4
3 b
3
5
b
3
1
5
y  x
3
3
Now how do we graph these equations?
First, look at the y-intercept. This will be
your starting point. Graph this point.
**Note** Your y-intercept will be on the y-axis
Once you have plotted the y-intercept, use
your slope to formulate the rest of the line.
Remember
Rise
Slope 
Run
Let’s Look at a Few Examples! 
 Graph the line y=-3x+5
 Graph the line y=2x+2
Now you try a Few Examples 
 Graph y=3x+2
 Graph y=-2x-4
What happens if….
What happens in our equation is not in
slope intercept form?
Sometimes our equations might be in
standard form.
Never fear, we can still graph them!!
How?
There are 2 ways we can go about
graphing an equation from standard form
First, we can try and find the x and y intercepts
of the line and plot those points and fill in the
line
Second, we can solve the equation and put it in
slope intercept form.
Let’s try
 Take the equation 4xy-7=0, for instance.
 First, get x and y alone:
4x-y=7
 To find the x intercept,
let y=0. So x=7/4
 To find the y intercept,
let x=0, so y=-7
 Therefore our 2 points
are (7/4, 0) and (0,-7)
 Use the same
equation and put it in
slope intercept form.
 4x-y=7
 4x=y+7
 y=4x-7
Both of these cases, we can graph.
When using standard form, plot the
points!
When using slope intercept form,
graph the intercept and then the
slope!
Let’s try together! 
 2x+3y=6
 Let x=0, y=2
 Let y=0, x=3
 x+4y-8=0
x+4y=8
 Let x=0, y=2
 Let y=0, x=8
Now you try!
 -2x+5y=10
 Let y=0, x=-5
 Let x=0, y=2
 3x+9y=9
 Let y=0, x=3
 Let x=0, y=1