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.
Ax + By ≥ C
Ax + By ≤ C
Ax + By > C
Ax + By < C
A solution of a linear inequality in two
variables, x and y, is an ordered pair
(x, y) that satisfies the inequality. The
solution to a linear inequality is a region of the
coordinate plane and is called a half-plane
bounded by a boundary line.
Graphing Linear Inequalities
1. Given a linear inequality in two variables,
graph its related linear equation.


For inequalities involving ≤ or ≥, use a solid
boundary line.
For inequalities involving < or >, use a
dashed boundary line.
2. Shade the appropriate region.




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,
shade to the left of the boundary line.
For inequalities in the form x ≥ c or x > c,
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
Dotted Line
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.
x is a vertical line
and
y is a horizontal line
a. x > -2
b. y ≤ -1
c. x ≤ -2
d. y > -1
Dotted Line
Writing Activities