Chapter 8 Unit Question How do inequalities affect algebraic concepts?

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Presentation transcript:

Chapter 8 Unit Question How do inequalities affect algebraic concepts?

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

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

Section 8 How do we graph linear Inequalities?

Homework Clicky

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

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

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 ?

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

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!

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

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

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 balloons streamers

Homework HoffmaSheet 8 – 8