Graphing Linear Equations

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Graphing Linear Equations

• From the beginning

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What is a Linear Equation?
A linear equation is an equation whose graph is a
LINE.
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What is a Linear Equation?
The equations we will be graphing have two
variables, x and y.
For example,
A solution to the equation is any ordered pair (x
, y) that makes the equation true.
The ordered pair (3 , 2) is a solution since,
If we were to plot all these ordered pairs on a
graph, we would be graphing a line.
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Graphing a Linear Equation
How do we graph linear equations?
Lets try this one y 3x 2
Make a Table of values
x y
2
1
0
1
2
8
y 3(2) 2 8
Complete the table by inputting the x - values
and calculating the corresponding y - values.
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y 3(1) 2 5
2
y 3(0) 2 2
1
y 3(1) 2 1
4
y 3(2) 2 4
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Graphing a Linear Equation
How about another one!
Lets try x 2y 5.
First Step Write y as a function of x
x 2y 5 2y 5 x
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Graphing a Linear Equation
How about another one!
Lets try x 2y 5.
Second Step Make a Table of Values
x y
2
1
0
1
3
2
8
Graphing Horizontal Vertical Lines
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
Graph x 3
y 2
Since there are no y values in this equation, x
is always 3 and y can be any other real number.
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