Download Graph an Inequality in Two Variables

GOAL
• Graphing linear inequalities in two variables
REMEMBER THE SYMBOLS




Less than
Greater than
Less than OR EQUAL TO
Greater than OR EQUAL TO
LINEAR INEQUALITIES
An example of a linear inequality in two variables is
x - 3y ≤ 6.
The solution of an inequality in two variables, x and y, is
an ordered pair (x, y) that produces a true statement
when substituted into the inequality.
Which ordered pair is NOT a solution of x - 3y ≤ 6?
A. (0,0)
B. (6,-1)
C. (10, 3)
D. (-1,2)
Substitute each point into the inequality. If the statement is true then it is a solution.
x - 3y ≤ 6
(0) – 3(0) ≤ 6
True, therefore
(0,0) is a solution.
GRAPH AN INEQUALITY
IN TWO VARIABLES
• The graph of an inequality in two variables is the set
of points that represent all solutions of the inequality.
• There is a BOUNDARY LINE that divides the
coordinate plane into two HALF-PLANES.
Only one half-plane contains the points that
represent the solutions to the inequality.
GRAPHING LINEAR INEQUALITIES
• Graphing Boundary Lines:
• Use a dashed line for < or >.
• Use a solid line for ≤ or ≥.
To graph the solution set for a linear inequality:
1. Graph the boundary line.
2. Select a test point, not on the boundary line, usually
the origin, (0,0) and determine if it is a solution.
3. Shade a half-plane.
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GRAPH AN INEQUALITY
Graph the inequality
STEP 1
Graph the equation
y  4x  3
STEP 2
Test (0,0) in the
original inequality.
y  4x  3
0  4(0)  3
True
y > 4x - 3.
STEP 3
Shade the half-plane that
contains the point (0,0),
because (0,0) is a solution
to the inequality.
GRAPH AN INEQUALITY
Graph the inequality
STEP 1
Graph the equation
x  2y  0
STEP 2
Test (1,0) in the
original inequality.
x  2y  0
1  2( 0)  0
False
x + 2y ≤ 0.
STEP 3
Shade the half-plane that
does not contain the
point (1,0), because (1,0)
is not a solution to the
inequality.
GRAPH AN INEQUALITY
Graph the inequality
STEP 1
Graph the equation
x  3 y  1
STEP 2
Test (1,0) in the
original inequality.
x  3 y  1
1  3(0)  1
True
x + 3y ≥ -1.
STEP 3
Shade the half-plane that
contains the point (1,0),
because (1,0) is a solution
to the inequality.
GRAPH AN INEQUALITY
Graph the inequality
STEP 1
Graph the equation
y  3
STEP 2
Test (2,0) in the
original inequality.
Use only the ycoordinate, because
the inequality does
not have a x-variable.
y  3
(0)  3
True
y ≥ -3.
STEP 3
Shade the half-plane that
contains the point (2,0),
because (2,0) is a solution
to the inequality.
GRAPH AN INEQUALITY
Graph the inequality
STEP 1
Graph the equation
x  1
STEP 2
Test (3,0) in the
original inequality.
Use only the ycoordinate, because
the inequality does
not have a x-variable.
x  1
( 0 )  1
False
x ≤ -1.
STEP 3
Shade the half-plane that
does not contain the
point (3,0), because (3,0)
is not a solution to the
inequality.