Graph Linear Equations
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Transcript Graph Linear Equations
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
23 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
47 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