1. Chapter 8 Unit Question How do inequalities affect algebraic concepts?

2. Open Learning Logs Date on Left…Section 8 – 8 on right

3. Then…Graph each line… 1.x = 3 2.y = -2 3.x = 0 4.y = -3x + 2 WARM UP 8 – 8 Draw a coordinate plane in your Learning Logs like the one on the white board

4. Section 8 How do we graph linear Inequalities?

5. Homework Clicky

6. To make sure we are OK, Graph : Up 3 Over 1 Up 3 Over 1

7. To make sure we are OK, Graph : Up 1 Over 2Up 1 Over 2

8. Graph this… If a point is on the y -axis, what is the value of x ? If a point is on the x -axis, what is the value of y ?

9. Remember rules for the dots when graphing on a number line? Solid dot for ≤ or ≥ to indicate point is included Open dot for to indicate point NOT included Linear inequalities are similar: Solid LINE for ≤ or ≥ to indicate line is included Dashed line for to indicate line NOT included

10. To help you decide which half- plane to shade, here is a HoffmaTrick!!!!! (Guaranteed to work unless the line goes through the origin) Graphing inequalities involves SHADING a half-plane. Pick a point and see if it solves the inequality. The ORIGIN is the easiest point to pick (0, 0) so…PICK IT!!!!! Substitute 0 for x and 0 for y. If the resulting sentence is true, shade to include the origin a.k.a. TOWARDS the origin If the resulting sentence is false, shade AWAY from the origin!

11. Graph 1st,substitute (0,0) and SHADE!!! Up 2 Over 1 Up 2 Over 1 Step 1: Is the line SOLID or DASHED? Step 2: Graph like any other slope-intercept line Step 3: Substitute ( 0, 0 ) True? Shade TOWARDS the origin

12. Graph 1st,substitute (0,0) and SHADE!!! Down 3 Over 1 Down 3 Over 1 Step 1: Is the line SOLID or DASHED? Step 2: Graph like any other slope-intercept line Step 3: Substitute ( 0, 0 ) True? Shade AWAY from the origin

13. WATCH OUT!!!!! How you shade depends on the problem!! Streamers: $2.00 per package Balloons: $1.50 per package The dance committee bought some of each and stayed within their $60 budget. Graph the possible scenarios! Write an inequality for the line… Let x = balloons y = streamers True? Shade TOWARD the origin 20 40 60 balloons streamers 40 30 20 10 0

14. Homework HoffmaSheet 8 – 8