Graphing Linear Equations
Slope – Intercept Form
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Slope
The slope of a line is the change in y
– values divided by the change in x –
values for any two points on the line.
Slope = change in y - values
change in x - values
y
Down 4
Rise = –4
Right 6
The above equation takes other
forms, such as
y2 - y1
Slope =
x2 - x1
where (x1 , y1) and (x2 , y2) are
any two points on the line.
x
Run = 6
Find thePick
change
anyintwo
yx – values
(RUN)points on the line
(RISE)
Slope is
On a graph, the slope can also be thought of as
Rise
Run
Rise = - 4 = - 2
Run
6
3
y - intercepts
y
The y – intercept is the y – value
when x = 0.
When using a graph, the y –
intercept is where the graph
crosses the y – axis.
The y – intercept of the line to
the right is …
y – intercept is 4.
x
Slope – Intercept Form
If you solve a linear equation for y, you will have put the equation in
slope – intercept form.
Slope intercept form is
y = mx + b
where (x , y) are again ordered pairs that make the equation true,
m is the slope of the line,
and b is the y – intercept of the line.
NOTE: m is the coefficient of x and b is just a constant value.
Slope – Intercept Form
Using our example from before
2x+ 3y = 12
We begin solving for y by subtracting 2x from both sides to obtain,
3y = - 2x+ 12
yTHINK
= mx + b
Dividing both sides by 3 gives us,
y=
Thus, the slope is
- 2 x+ 4
3
- 2
and the y – intercept is 4.
3
Graphing y = mx + b
y
Let's graph one!
Down 2
STEPS TO GRAPHING
Right 1
Step 1: Put equation in slope
intercept form
Down 2
Right 1
Step 2: Plot the y –intercept
on the graph
Step 3: Starting at the y – intercept,
use the slope to find other points,
then connect the points.
Graph y = –2x + 5
x
Slope = –2 means
- 2
1
This equation is already in slope – intercept form.
Graphing ax + by = c
What about 3x + 4y = –12 ?
y
Step 1: Put equation in slope –
intercept form
This means solve for y.
y = - 3- 3 x
4
Step 2: Plot the y – intercept.
Step 3: Starting at the y –
intercept, use the slope to find
other points.
3
A slope of - means
4
Down 3, Right 4…or…Up 3, Left 4 (the 3 or 4 can be negative, but not both).
x