Download Unit 7 Day 2 Notes Graphing inequalities with 2 variables

Algebra Part 3
Unit 7
Name____________________________
Date________________
Warm-up
Solve the following absolute value equations and graph your solutions.
1.
x−5 ≥7
2.
x−4
≤ 6
Guided Notes
Unit 7 – Graph Linear Inequalities In Two Variables
Review
Graph the linear equations.
1) y = 2x – 3
2
2) y = − x + 1
3
3) 3x – 2y = 6
A linear inequality in two variables is a result of replacing the ______ sign in a linear
equation with _____, _____, _____, _____. A solution of an inequality in two variables x
and y, is an ordered pair (
,
) that produces a __________ statement where the values
of x and y are ____________________ into the inequality.
Is (8,3) a solution to x – y < 5?
In a coordinate plane, the graph of an inequality in two variables is the set of points
that represents ___________________ of the inequality. The _________________ __________
of a linear inequality divides the coordinate plane into ______ _________ ___________. Only
one of the half-plane contains the points that represents the _______________ of the
inequality.
Key Concept:
Graphing a Linear Inequality in Two Variables
Step 1: Graph the boundary line. Use a dashed line
line
for ≥ or ≤.
for < or > and use a solid
Step 2: Shade above if the inequality symbol is ________ or _________. Shade below if the
inequality symbol is _________ or ________.
***YOU CAN ONLY USE THE SHADING RULES ABOVE IF THE EQUATION IS IN
SLOPE-INTERCEPT FORM!!!
Examples
Graph the inequality.
1) y > 4x – 3
2) y ≥
3
x +3
4
3) y <
1
x+4
3
4) 3x – y > 2
7) x ≤ 2
Homework: Worksheet
5) 2x + 4y = -8
6) x + y = -4
8) y > -4