Download Section 8.4

Section 8.4
Graphing Linear Equations
in Two Variables
Linear Equation in Two
Variables
A linear equation in two variables is an
equation that can be written in the form
ax + by = c
where a, b, and c are numbers, and a
and b are not both 0.
Examples
3x + 2y = 6
y=8
Martin-Gay, Prealgebra, 5ed
3x = 4
Graphing Linear Equations
by Plotting Points
Every linear equation in two variables has
infinitely many ordered-pair solutions. Since
it is impossible to list every solution, we
graph the solutions instead.
The pattern described by the solutions of a
linear equation makes “seeing” the solutions
possible by graphing because all the
solutions of a linear equation in two variables
correspond to points on a single straight line.
If we plot a few of these points and draw the
straight line connecting them, we have a
complete graph of all the solutions.
Martin-Gay, Prealgebra, 5ed
To graph the equation x + y = 5, we plot a
few ordered-pair solutions, say (2,3), (0,5),
and (-1, 6). Then we connect the points.
y
(-1,6)
5
4
3
2
1
(0,5)
(2,3)
x
-5 -4 -3 -2 -1
1 2 3 4 5
Martin-Gay, Prealgebra, 5ed
To Graph a Linear Equation in
Two Variables
Find three ordered-pair solutions.
 Graph the solutions.
 Draw a line through the plotted points.

Martin-Gay, Prealgebra, 5ed
To Find an Ordered-Pair
Solution of an Equation
Choose either an x-value or y-value of the
ordered pair.
 Complete the ordered pair by replacing
the variable with the chosen value and
solving for the unknown variable.

Martin-Gay, Prealgebra, 5ed
Helpful Hint
All three points should fall on the
same straight line. If not, check your
ordered-pair solutions for a mistake,
since every linear equation is a line.
Martin-Gay, Prealgebra, 5ed
Horizontal Lines/Vertical Lines
y
y
x
y=b
x
x=a
Martin-Gay, Prealgebra, 5ed