2.1 Graphing Linear Equations

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2.1 Graphing Linear Equations
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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 this 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 y 3x 2
Make a table (or T-chart)
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.
5
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
Now lets try x 2y 5.
First Step Write y as a function of x
x 2y 5 2y x 5
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Graphing a Linear Equation
Lets continue with x 2y 5
Second Step Make a table
x y
2
1
0
1
3
2
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Find INTERCEPT points for a graph to help with
graphing

• To find the x-intercept set y 0 (x,0)
• To find the y-intercept set x 0 (0,y)

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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
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Midpoint formula
The midpoint is half-way between the two points
The midpoint formula can be thought of as
(average of x values, average of y values), or
.
So we average the x and y values to get the
midpoint.