6.5 Linear Inequalities

1. 6.5 Linear Inequalities I can graph linear inequalities in two variables and use linear inequalities when modeling real-world situations.

2. Solution of a Linear Inequality • 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.

3. Practice • 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 > -2 • Check if this is true: yes! It is a solution. • (-3,-7) • No! This is not a solution.

4. Graphing a Linear Inequality • It should still be in slope-intercept form • So 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 line • If y is less than, shade below the line.

5. You Try! • What is the graph of y > x – 2? • Graph y = x – 2 • Use a dashed line • Shade above the line since it is greater than

6. Graphing in One variable • What is the graph of x > -1? • Graph x = -1 • Use a dashed line • Shade to the right since x is greater than

7. You try! • What is the graph of y ≥ 2?

8. Modeling with inequalities • 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 inequality • 24x + 12y ≤ 420 • Write in slope-int form • y ≤ -2x +35 • Graph and pick 3 solutions. • $5 and $5 • $10 and $10 • $5 and $20

9. Assignment • Odds p.397 #9-37