I can graph l inear inequal i t ies in two variables and use l inear inequal i t ies when model ing real-world s i tuat ions.

6.5 LINEAR INEQUALITIES

A linear inequality in two variables (ex: y > x – 3) can be formed by replacing the equal sign with an inequality symbol.

A solution of an inequality is an ordered pair (x,y) that makes the inequality true.

SOLUTION OF A LINEAR INEQUALITY

Is the ordered pair a solution to the inequality y > x – 3?

(1,2)Substitute values for x and y: 2 > 1 – 3 Simplify: 2 > -2Check if this is true: yes! It is a solution.

(-3,-7)No! This is not a solution.

PRACTICE

It should still be in slope-intercept formSo we still use a slope and y-intercept to graph.

Use a dashed line if > or < but not equal to

Use a solid line if ≤ or ≥If y is greater than, shade above the

lineIf y is less than, shade below the line.

GRAPHING A LINEAR INEQUALITY

What is the graph of y > x – 2?Graph y = x – 2Use a dashed lineShade above the line since it is greater

than

YOU TRY!

What is the graph of x > -1?

Graph x = -1Use a dashed lineShade to the right since x is greater

than

GRAPHING IN ONE VARIABLE

What is the graph of y ≥ 2?

YOU TRY!

An interior decorator will remodel the kitchen as shown and can only spend $420 or less. What are 3 possible prices for wallpaper and tile?

Write an inequality24x + 12y ≤ 420

Write in slope-int formy ≤ -2x +35

Graph and pick 3 solutions. $5 and $5 $10 and $10 $5 and $20

MODELING WITH INEQUALITIES

Odds p.397 #9-37

ASSIGNMENT