Name: Date: Topic: Linear Inequalities Essential Question: How can the infinite number of solutions of a linear inequality be represented? Warm-Up: Graph the following linear equations: n y = - 2x + 3 n y = 3x n 4x + y = 5 n y = 2 n x = - 3 Suggestion: Refer to your notes on graphing linear equation if needed!

Exam #7 - Review

Lets identify possible solutions Is the ordered pair a solution of y > x – 3? A) (1, 2) B) (- 3, - 7) Is the ordered pair a solution of y ≤ + 4? A) (- 6, 4) B) (3, 6)

Graphing a Linear Inequality 1) Solve the inequality for y (or for x if there is no y). 2) In your head/mind change the inequality to an equation and graph (on paper if it helps you understand better). 3) If the inequality is, the line is dotted (-----). If the inequality is ≤ or ≥, the line is solid ( ).

Graphing a Linear Inequality Graph the inequality: 3 - x > 0  What should we do first?  Because x < 3 and not x ≤ 3, the line will be dotted. Now shade the side of the line where x < 3 (to the left of the line).

Graphing a Linear Inequality n Pick a point, (1,2), in the shaded area. n Substitute into the original inequality 3 – x > 0 3 – 1 > 0 2 > 0 n True! The inequality has been graphed correctly ) To check that the shading is correct, pick a point in the area and plug it into the inequality. 5) If the inequality statement is true, the shading is correct. If the inequality statement is false, the shading is incorrect.

Graphing an Inequality Graph x < 2 Now what points would give you less than 2? Since it has to be x < 2 we shade everything to the left of the line. Only for values of “X”

Graphing a Linear Inequality Sketch a graph of y  3

Some Helpful Hints If the sign is > or < the line is dotted (-----) If the sign is  or  the line will be solid When dealing with just x and y. If the sign > or  the shading either goes up or to the right If the sign is < or  the shading either goes down or to the left

Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y <-x + 3 Step 2: Graph the line y < -x + 3 Step 3: Shade your solution

When dealing with slanted lines If it is > or  then you shade above If it is < or  then you shade below the line

Lets See if you Really Understand Practice Time!!! Page (1 – 4, 16, 20, 22, 32, 33, 42)

Wrap-Up:  Review Key Concepts  EOC Like questions Ensure that all problems from 51 to 70 are completed You will not earn credit if: -You do not show work -Any question are unanswered