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Graphing Linear Equations
From the beginning
What is a Linear Equation?
y
A linear equation is an equation whose
graph is a LINE.
x
Not Linear
Linear
What is a Linear Equation?
y
The equations we will be graphing have
two variables, x and y.
For example,
2x+ 3y = 12
A solution to the equation is any
ordered pair (x, y) that makes the
equation true.
x
The ordered pair (3 , 2) is a
solution since,
2(3)+ 3(2)= 12
If we were to plot all these ordered
pairs on a graph, we would be graphing 2 0 + 3 4 = 12
() ()
a line.
2(- 3)+ 3(6)= 12
2(6)+ 3(0)= 12
2(- 1)+ 3 4 2 = 12
3
( )
Graphing a Linear Equation
y
How do we graph linear equations?
Let’s try this one: y = 3x – 2
Make a Table of values
x
y
–2
–8
–1
–5
0
–2
1
1
2
4
y = 3(–2) – 2
x
y = –8
y = 3(–1)
2
Complete
the–table
by inputting
y = –5 the x values and
calculating
y = 3(0)the
–2
corresponding y y= –2
values.
y = 3(1) – 2
y = 3(2) – 2
y= 1
y= 4
The x - values are picked by YOU!
Graphing a Linear Equation
y
How about another one!
Let’s try y = 5-2x.
First Step:
Make a Table of Values
x
y
–2
9
–1
8
0
5
1
3
2
1
Take a
moment
and
complete
the chart…
x
Graphing Horizontal & Vertical Lines
y
When you are asked to graph a line,
and there is only ONE variable in the
equation, the line will either be
vertical or horizontal. For example …
x
Graph x = 3
Since there are no y – values in this
equation, x is always 3 and y can be
any other real number.
y = –2
Graph y = –2
Since there are no x – values in this
equation, y is always – 2 and x can
be any other real number.
x=3