# Linear Inequalities ```A.REI.12
Graphing linear inequalities
Name: _______________________
Activator
Is the Point a Solution?
Directions:
1) On the coordinate plane below, graph the line x – 2y = 8.
2) Determine if each of the given points is a solution of the inequality x – 2y &lt; 8 by
substituting the x- and y-coordinates into the inequality.
a. If it is a solution, plot a Y for “yes” at the given coordinates.
b. If it is not a solution, plot an N for “no” at the given coordinates.
3) Answer the questions that follow.
Split this work with your table partners to speed it up!
(0, 0)
(-6, -7)
(0, -5)
(4, -6)
(3, 3)
(8, 0)
(-3, -9)
(-4, 2)
(1, -6)
(9, -2)
(-4, -6)
(0, 6)
(5, -3)
(-8, -4)
(-8, -10)
(8, 8)
Questions:
1) What do you notice about
where the Ys and Ns are?
2) Why is x – 2y = 8 called a
“boundary line”?
3) How would this picture
change if the inequality had been
x – 2y &lt; 8 instead of x – 2y &lt; 8?
Support - A.REI.12
**Guided notes organizer on pages 6 &amp; 7 **
Name: _______________________
Practice Graphing Linear Inequalities
1) Determine if each point is a solution to the inequality 3x – 4y &gt; 8 by using the graph shown.
a) (3, -4)
b) (4, 1)
c) (-3, -4)
d) (0, 0)
e) (-4, -5)
f) (1, -10)
g) (-1.5, -5)
a) (3, -4)
b) (4, 1)
c) (-3, -4)
d) (0, 0)
e) (-4, -5)
f) (1, -10)
g) (-1.5, -5)
3) Graph each inequality. Pay attention to the type of boundary line you need.
a) y &gt; -2.5
b) x &lt; -2.5
c) |y| &lt; 1
d) |x| &gt; 1
e) 5y – 2x &lt; 9
f) y &gt; -2&frac12; – &frac34;x
g) y &lt; -4x + 3
h) 10x – 8y &gt; 24
On Target - A.REI.12
Name: _______________________
Graphing Linear Inequalities
1) Determine whether each point is a solution to the
inequality that is shown in the graph to the right.
a) (1, 2)
b) (4, 3)
c) (2, -2)
d) (-4, 0)
e) (3.27, -4.03)
f) (0, -3)
g) (10, -5)
h) (0, -5)
2) Given the inequality 4x + 5y &gt; 12, determine algebraically if each point is a solution or not.
a. (-2, 4)
b. (3, -2)
c. (0, 2)
d. (2, 5)
3) Graph the inequality from problem 2 on
the coordinate plane to the right. Use the
intercepts method to make the graph.
problem 2 are correct.
5) Use the graph to determine if these points
are solutions to 4x + 5y &gt; 12:
a. (3.7, 2.15)
b. (-2, 4.88)
c. (5.6, -3.99)
d. (0, 0)
6) Graph each inequality. Pay attention to the type of boundary line you need.
a) y &lt; 3.5
b) x &gt; -2.5
c) |x| &gt; 2
d) |y| &lt; 4
e) y &gt; -4 – 2x
f) -2x – 4y &gt; 10
Extension
Graph:
1) y &lt; (x – 2)2 – 3
2) y &gt; |x + 2| – 2
Lesson Name: Linear Inequalities
Date: _________________ Student: ___________________________
Support Notes: Systems
Concepts
Examples
y4
x  1
y 3
of Equations and Inequalities
Background Information
Concepts
Examples
x 4
y  2x  3
4x  5y  10
Background Information
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