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Graphing linear
equations
By
Robert O. Mills Jr.
Hermitage High School
Henrico County Public Schools
Part One
Solving for
Y
In order to graph
a linear equation
you must first
solve for y.
Given the Problem :
First check to see if y
is + or –.
x+y=4
If y is + you leave it alone.
What number or factor is on the
same side of the equation as + y?
x+y=4
Move that number or
factor to the other side of
the = and change its sign.
x+y=4
Move that number or
factor to the other side of
the = and change its sign.
y=4-x
Your answer is:
y=4-x
Given the Problem :
First check to see if y
is + or –.
x-y=4
If y is - you move y to the
other side of the = and
change it to +y.
What number or factor is on the
same side of the equation as + y?
x=4+y
Move that number
or factor to the
other side of the =
and change its
sign.
x=4+y
Your answer is:
x-4 =y
or
y=x-4
Given the Problem :
x+2y=4
First check to see if y
is + or –.
x+2y=4
If y is + you leave it alone.
What number or factor is on the
same side of the equation as + y?
x+2y=4
Move that number or
factor to the other side of
the = and change its sign.
x+2y=4
Move that number or
factor to the other side of
the = and change its sign.
2y=4-x
If the +y factor has a co-efficient it
must lose it. The factors and
numbers on the opposite side of the
= become a fraction with the y coefficient as the denominator.
2y=4-x
If the +y factor has a co-efficient it
must lose it. The factors and
numbers on the opposite side of the
= become a fraction with the y coefficient as the denominator.
4x
y
2
Given the Problem :
2x-2y=4
First check to see if y
is + or –.
2x-2y=4
If y is - you move y to the
other side of the = and
change it to +y.
2x-2y=4
2x=4+2y
What number or factor is on the
same side of the equation as + y?
2x=4+2y
Move that number
or factor to the
other side of the =
and change its
sign.
2x=4+2y
2x-4 =2y
Your answer is:
2x-4 =2y
or
2y=2x-4
If the +y factor has a co-efficient it
must lose it. The factors and
numbers on the opposite side of the
= become a fraction with the y coefficient as the denominator.
2y=2x-4
If the +y factor has a co-efficient it
must lose it. The factors and
numbers on the opposite side of the
= become a fraction with the y coefficient as the denominator.
2x  4
y
2
Advanced Level
• There are times when it will be
necessary to work the equation to a
simpler level.
• For example the formula for slope
intercept is y = mx + b. Any denominator
in this case must be eliminated. How to
do this?
Most often when we think of the
distributive property, we are thinking of
using it with ( ) and the operation is
multiplication.
2x  4
In the previous example y  2
the
line is also a grouping tool with the
operation division.
2x  4
y 
2
2x
4
y 

2
2
y x2
This is a more complex problem.
x4
y
2
x  4
y 
2
x
4
y 

2
2
2
y
x2
1