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```4.2 Graphing Linear Equations
Goal
Graph a linear equation using a table of values.
VOCABULARY
Linear equation A linear equation in two variables x and y is
an equation that can be written in the form Ax By C,
C
where A and B are not both zero.
Solution of an equation A solution of an equation in two
variables x and y is an ordered pair (x,
x y
y) that makes the
equation true.
Function form A two-variable equation is in function form if
one of its variables is isolated on one side of the equation.
Graph of an equation The graph of an equation in two
variables x and y is the set of all points (x,
x y
y) that are
solutions of the equation.
Example 1
Check Solutions of Linear Equations
Determine whether the ordered pair is a solution of 2x 3y 6.
a. (3, 4)
b. (4, 1)
Solution
a.
Write original equation.
2x 3y 6
2( 3 ) 3( 4 ) ⱨ 6
6
b.
6
Substitute 3 for x and 4 for y.
Simplify. True
statement.
a solution of the equation 2x 3y 6.
2x 3y 6
2( 4 ) 3( 1 ) ⱨ 6
5 6
Write original equation.
Substitute 4 for x and 1 for y.
Simplify. Not a true statement.
Answer (4, 1) is not a solution of the equation 2x 3y 6.
a division of Houghton Mifflin Company.
Chapter 4 • Algebra 1, Concepts and Skills
Notetaking Guide
80
Checkpoint Determine whether the ordered pair is a solution
2 y 3.
of 2x
1. (0, 3)
2. (1, 1)
Solution
Example 2
3. (1, 5)
Not a solution
Solution
FFind Solutions of Linear Equations
Find three ordered pairs that are solutions of 5x
5 y 2.
1. Rewrite the equation in function form to make it easier to
substitute values into the equation.
5x
5 y 2
Write original equation.
y 5x 2
2. Choose any value for x and substitute it into the equation to find
the corresponding yy-value. The easiest xx-value is 0 .
y 5( 0 ) 2
Substitute 0 for x.
y 2
Simplify. The solution is (0, 2) .
3. Select a few more values of x and make a table to record
the solutions.
x
0
1
2
3
1
2
y
2
3
8
13
7
12
Answer (0, 2) , (1, 3) , and (1, 7) are three solutions
of 5x
5 y 2.
a division of Houghton Mifflin Company.
Chapter 4 • Algebra 1, Concepts and Skills
Notetaking Guide
81
GRAPHING A LINEAR EQUATION
Step 1 Rewrite the equation in function form, if necessary.
Step 2 Choose a few values of x and make a table of values .
Step 3 Plot the points from the table of values. A line through
these points is the graph of the equation.
Example 3
Graph a Linear Equation
Use a table of values to graph the equation x 4y 4.
1. Rewrite the equation in function form by solving for y.
x 4y 4
Write original equation.
4y x 4
Subtract x from each side.
1
y x 1
Divide each side by 4 .
4
2. Choose a few values of x and make a table of values.
When graphing
a linear equation, try
choosing values of x
that include negative
values, zero, and
positive values to
see how the graph
behaves to the left
and right of the
y-axis.
x
4
0
4
y
2
1
0
y
3
1
You have found three solutions.
Y
3
1
1
1
3
x
(4, 2 ), (0, 1 ), (4, 0 )
3
3. Plot the points and draw a line
through them.
Checkpoint Complete the following exercise.
4. Use a table of values to graph the
equation x 2y 1.
y
3
1
3
1
1
1
3
x
3