Transcript 3.1 Linear Inequalities in Two Variables

3.3 Linear Inequalities in
Two Variables
Objectives: Solve and graph a linear
inequality in two variables.
Use a linear inequality in two variables
to solve real-world problems.
Standard: 2.8.11.K. Apply an appropriate technique
to graph a linear inequality.
A linear inequality in two
variables, x and y, is any inequality
that can be written in one of the forms
below, where A ≠ 0 and B ≠ 0.
A x + By ≥ C
Ax + By ≤ C
Ax + By > C
Ax + By < C
• A solution of a linear inequality is the value of
the variables (x, y) that make the inequality a
true statement.
• When graphed on a coordinate plane the
solution to a linear inequality is a region called
a half-plane and is bordered by a boundary
line.
Graphing Linear Inequalities
1. When graphing a linear inequality with
two variables, graph the border line as if
it were a linear equation.
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For inequalities involving ≤ or ≥, use a solid
boundary line.
For inequalities involving < or >, use a
dashed boundary line.
2. After graphing the border line, shade the
appropriate region.
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For inequalities in the form of y ≤ mx + b or
y < mx + b, shade below the boundary line.
For inequalities of the form y ≥ mx + b or
y > mx + b, shade above the boundary line.
For inequalities in the form x ≤ c or x < c
(vertical lines), shade to the left of the
boundary line.
For inequalities in the form x ≥ c or x > c
(vertical lines), shade to the right of the
boundary line.
Ex 1. Graph each linear
inequality.

a. y < x + 2
b. y ≥ -2x + 3
* c. y > -2x - 2
d. y ≥ 2x + 5
e. -2x –3y ≤ 3
f. 3x – 4y ≥ 4
-4y≥-3x + 4
y≤¾x-1
g. -5x – 2y > 4
-2y > 5x + 4
y < -5/2 x - 2
Dotted Line
Ex 3. Graph each linear inequality.
Horizontal line:
y > a constant
y < a constant
y < a constant
y > a constant
Vertical line:
x > a constant
x < a constant
x < a constant
x > a constant
a. x > -2
b. y ≤ -1
c. x ≤ -2
d. y > -1
Writing Activities