+
Lesson 6-5
Linear Inequalities
November 17, 2014
+
Daily Learning Target
I
will graph linear inequalities in two
variables.
I
will use linear inequalities when modeling
real-world situations.
+
Vocabulary
Linear
inequality
Describes a region of the coordinate
plane that has a boundary line
Solution
of an inequality
Coordinates of the plane that makes
the inequality true
Example 1: In Notes
Tell whether the ordered pair is a solution of the
inequality.
(–2, 4); y < 2x + 1
Independent Practice #1
Tell whether the ordered pair is a solution of the
inequality.
(3, 1); y > x – 4
Graphing Linear Inequalities
Step 1
Solve the inequality for y (slope-intercept
form). ( y=mx+b)
Step 2
Graph the boundary line. Use a solid line for ≤
or ≥. Use a dashed line for < or >.
Step 3
Shade the half-plane above the line for y > or ≥.
Shade the half-plane below the line for y < or y ≤.
Check your answer.
Example 2: Write in your Notes
Graph the solutions of the linear inequality.
y  2x – 3
Step 1 The inequality is
already solved for y.
Step 2 Graph the boundary
line y = 2x – 3. Use a solid
line for .
Step 3 The inequality is , so
shade below the line.
+
Independent Response
 How
do you know when you shade above or
below the boundary line?
 When
do you use a dotted boundary line?
 When
do you use a solid boundary line?
Independent Practice #2
Graph the solutions of the linear inequality. Check
your answer.
Example 3: Writing an Inequality from a Graph
Write an inequality to represent the graph.
Independent Practice #3
Write an inequality to represent the graph.
+
Special Cases
Y>
3
Zero slope
X<
-2
Undefined slope
Ex 4: Graphing in Standard Form
Write this in your notes
Graph the solutions of the linear inequality. Check
your answer.
5x + 2y > –8
Word Problem!: Notes
For a party, you can spend no more than $12 on nuts.
Peanuts cost $2/lb. Cashews cost $4/lb. What are
three possible combinations of peanuts and cashews
you can buy?
Word Problem!: Independent Practice #4
Ada has at most 285 beads to make jewelry. A
necklace requires 40 beads, and a bracelet requires
15 beads.
Let x represent the number of necklaces and y the
number of bracelets.
Write an inequality. Use ≤ for
at most.