Practice converting linear
equations into SlopeIntercept Form
It’s easier than you think…
Focus 7 - Learning Goal #1: The student will understand the
connections between proportional relationships, lines, and linear
equations and use functions to model relationships between quantities.
4
In addition to level
3.0 and beyond
what was taught in
class, the student
may:
 Make
connection with
other concepts
in math.
 Make
connection with
other content
areas.
3
The student will
demonstrate and
explain the
connections
between
proportional
relationships,
lines, and linear
equations and use
functions to
model
relationships
between
quantities.
2
The student
will
demonstrate
and identify
proportional
relationships,
lines, and
linear
equations and
use functions
to model
quantities.
1
With help
from the
teacher,
the student
has
partial
success
with level 2
and 3
elements.
0
Even with
help,
students
have no
success with
level 2 and 3
content.
Slope intercept form is:
y = mx + b
Our main goal is to get the y
alone on one side of the
equation
Convert Into Slope-Intercept Form
2 y  4x  2
(divide both sides by 2 to get y alone)
2 y  4x  2
2
2
2
(now simplify all fractions)
1
2 y  4x  2
2
2
2
y  2x 1
When an equation is in slope-intercept
form:
Now look at the equation below……
y  2x 1
What is the slope? ____________
What is the intercept? ____________
Now look at the graph of the line.
Step 1: Look at the y-intercept and plot
where the graphs cross the “y” axis.
Step 2: Use the slope
(rise/run) to determine
the next point and plot.
Step 3: Draw a line
through both points. Be
sure to extend pass point
and put arrow at both
ends.
5
4
3
2
1
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
2
3
4
5
*** Easy ***
Convert to Slope-Intercept Form:
5y = 10x + 15
(divide both sides by 5 to get y alone)
5 y  10 x  15
5
5
5 y  10 x  15
5
5
5
(now simplify all fractions)
y = 2x + 3 BRAVO!!
*** Now Try this Convert to
Slope-Intercept Form ***
-3y = -9x - 12
Step 1: divide both sides by -3 to get y alone
Step 2: Simplify all fractions
Step 3: Write your equation in y = mx + b
What is the slope? ____________
What is the intercept? ____________
*** Check Your Answer ***
-3y = -9x - 12
-3
-3
(divide both sides by -3 to get y alone)
(now simplify all fractions)
-3y = -9x - 12
-3
-3 -3
y = 3x + 4
Slope = 3
Intercept = 4
Wow, you’re good
at this!!
*** medium ***
Convert to Slope-Intercept Form:
21x – 7y =14
(subtract both sides by 21x)
21x
-21x
(now divide both sides by -7)
-7y = -21x + 14
7 - 7 -7
y = 3x – 2
(simplify all fractions)
*** Now Try this Convert to SlopeIntercept Form ***
2y + 26 = -6x
Step 1: Subtract both sides by 26
Step 2: Divide both sides by 2 to get y by itself
Step 3: Simplify all fractions
What is the slope? ____________
What is the intercept? ____________
*** Check Your Answer ***
2y + 26 = -6x
(subtract both sides by 26)
26
-26
(now divide both sides by 2
2y = -6x - 26
2
2 2
(simplify all fractions)
y = -3x - 13
You are a math wizard!
Graphing from the slopeintercept form
• Graph y = ½ x + 2
• Locate the y-intercept on the graph
and plot the point.
Plotting the second point
using the slope ½
changein y rise 1


changeinx run 2
• Move up 1 and right 2 and plot the
second point.
Plotting the slope
Drawing the line
• Now use a straight edge and connect
the two points.
• You can check your work, by choosing
any point located on the line and
substituting the point into the
equation. The equation will be true
no matter what point you chose.