This lesson teaches how to graph equations in y = mx + b form and also teaches three forms of the equation of a line.

1. Skill31B Graphing Lines from Slope-Intercept Form and three forms of the
Equation of a line pages 165-166a
Last lesson we looked at reading the slope of a line from the y = mx + b form of a line.
This lesson will add graphing the line to that concept. In addition, we will look at
three forms of the equation of a line. All three may be on the test; however, the
y = mx + b form is the most common.
In the last lesson you found the slope by looking for the m value (m is the symbol
for slope in the equations we are using. Now we will use the other value, b, to find a
starting place to graph on the y axis. We will rework the problems from page 165 but graph
this time.

2. Graph each line from page 165..
How? Start at +1 on
the y-axis. Then go up 2
And right 3 to another point.
How? Realize that the
Y-intercept, the b number,
Is -3. Graph a point there.
Then use the slope, ½, to go
Up 1 and right 2 to another
Point. Draw the line.
How? Identify +2 as
the y-intercept. Graph
a point at 2 on the y axis.
Use the slope, -3/4, to
go down 3 and right 4
For another point.
Draw the line.

3. Graph these.
Look for b. b is -2
Start there on the
Y axis. Use the slope,
m , 4/1 to plot the next
point by going up 4 and
right 1.
b is +2. Start there.
m is -1/4. From 2 go
Down 1 and right 4.
It looks like the b number
Is missing. It is 0. Start at
0. Then use the slope,
5/3 to go up 5 and right
3.

4. Now we will look at three forms of the equation of a line. These are three ways
to say the same thing. They just have the information presented in
dfferent ways.
1. Slope Intercept This is the one we have used already. Y = mx + b Read below for
a summary.
2. Point-slope form. This one is on the formula sheet for the test.
It gives the slope, m, and a point to start graphing. This point is not on the y-axis. Just
graph it and use the slope from there to get another point.
(y – y1) = m (x – x1) Example. Y – 3 = 4 ( x -2) slope is 4 Starting point is (2,3).
Notice the x,y order.
Example. Y + 8 = -3 (x -4) Slope is -3. Starting point is (4, -8).
Notice that the starting point has +4 for
x and -8 for y.

5. More point slope with a graph.
Y – 2 = 2/3 (x + 1) The starting point is (-1, 2) and the slope is 2/3.
The starting point is
(-1,2). Then go up 2
And right 3.
Just be ready to identify the slope and point to start from in a question.
Notice the formula has y – y1 so if you have y – 2 the y of the starting point is 2.
If you have y + 3 the y of the starting point is -3.

6. The Standard Form of a Line
All the line we have looked at can also be written in a different form called Standard
Form. This is Ax + By = C. Here the x and y terms are on the same side of the equals
sign with the x part first. The number C is on the other side by itself. This form of the line
is useful in other kinds of problems but can be used to find the slope and y-intercept
with these definitions.
The slope is the opposite of A/B. Just put the
A number over the B number and change the
sign. Note that this B number is not the same
as the number for the y-intercept in the slope-
intercept form.
The y-intercept is just the C number over the B
number.
Example. 2x + 3y = 4 So the slope is -2/3. The y-intercept is 4/2 or just 2.
That’s it!! The bad part is that the definitions of m and the y-intercept are not
on the formula sheet. You have to learn them.
Sometimes on the test, they may give you 2x + 3y = 4 and just ask for the slope.

7. Find the slope and y-intercept for these lines written in Standard Form.
X + 5 y = 10 slope is -1/5 y – intercept is 10/5 or just 2
3 x – 2 y = 6 slope is –(3/-2) or + 3/2 y – intercept is 6/-2 or 3/-1 or just -3
X - y = -4 slope is –(1/-1) or –(-1) or +1 y-intercept is -4/-1 or +4

8. To close today’s lesson, I am going to show you the same line written
In all three forms and graph it. You would never be expected to work with all three at
once. This is just to help you see if this all makes sense.
Y = -x + 4 Slope intercept form
m = -1 and b = 4 Start at 4, then
Go down 1 and right 1.
Point-slope form
Y – 1 = -(x -3) slope is -1 and starting
point is (3, 1)
Standard Form
X + y = 4 slope is -1/1 or -1
y –Intercept is 4/1 or 4
See they are all the same line!!
The y-intercept 4