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Graphing Linear Inequalities.

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Presentation on theme: "Graphing Linear Inequalities."— Presentation transcript:

1 Graphing Linear Inequalities

2 We show the solution to a linear inequality with a graph.
Step 1) Put the inequalities into slope-intercept form. y = mx + b slope y-intercept

3 Step 2) Graph the line If the inequality is < or >, make the lines dotted. If the inequality is < or >, make the lines solid.

4 Step 3) Shade the correct region of the graph:
Above the line b) Below the line for y > or y . for y < or y ≤. **This is because more then 1 ordered pair can be a solution!

5 Examples: 1) y > -5x + 4

6 Examples: 2) x < ) y ≥ -3

7 Examples: 4) 2x – 3y ≤ 6

8 Examples: 5) 3x + 2y < -2

9 Systems of Inequalities

10 We show the solution to a system of linear inequalities with a graph!

11 Steps to Graphing a System of Inequalities:
Put the inequalities into slope-intercept form. Decide if the lines should be dotted or solid Shade above for y > or y , shade below for y < or y ≤. Shade the overlapping section darker to show where the solutions to both inequalities lie.

12 Example #1: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

13 Graph each line, make dotted or solid and shade the correct area.
Example, continued: Graph each line, make dotted or solid and shade the correct area. a: dotted shade above b: dotted shade below

14

15 #2 Graph the system of linear inequalities.
x ³ –1 y > x – 2

16 #3 x > -2 y < 6 -2x + y > -5

17 Let’s graph the next problem using the calculator #4 y ≥ -x + 4 y < 3x - 2

18 #5 x – y > 3 7x – y ≤ -3

19 #6 7x + 2y < -10 -x + 2y ≤ 11

20 Classwork: Solving Systems of Inequalities Worksheet Homework: Unit 7 TEST -


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