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Graphing Linear Inequalities in Two Variables

LESSON ESSENTIAL QUESTION: How do you graph an inequality?WARMUPComplete Day 4 Warmup Problems

Shade, Shade, Shade, Shade Ithttp://teachertube.com/viewVideo.php?video_id=121267

Graphing ReviewGraph each line.a) y = x + 2b) x 2y = 6

Put the equations into y=mx+b form to graph!

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Graphing InequalitiesWhere do you think the points that are y > x + 2 are located?

Where do you think the points that are y < x + 2 are located?Graphing InequalitiesThe line is the boundary of the two regions. The blue region is the greater than (>) area and the yellow region is the less than ( x + 2. And, the yellow could be represented by y < x + 2.

Tell Your NeighborWhat does it mean to be a point in the solution of an inequality?A point in the shaded area of the solution set that fits the inequalityName 1 point in the solution setName 1 point NOT in the solution set

Steps to Graphing Linear Inequalities1. Change the inequality into slope-intercept form, y = mx + b. Graph the equation.2. If > or < then the line should be dashed. If > or < then the line should be solid.3. If y > mx+b or y > mx+b, shade above the line.If y < mx+b or y < mx+b, shade below the line.To check that the shading is correct, pick a point in the area and plug it into the inequalityIf TRUE, you shaded correctIf FALSE, you shaded incorrectlyGRAPHING INEQUALITIESINEQUALITYSYMBOLTYPE OF LINE(dashed or solid)WHERE TO SHADE(above or below line)

dashedbelowdashedabovesolidbelowsolidabove

GRAPHING INEQUALITIESSHADE UPSHADE BELOWSOLID LINEDASHED LINE> or then you shade above

If it is < or then you shade below the lineGraph y -3x + 2 on the coordinate plane.xy

Boundary Liney = -3x + 2m = -3b = 2

Test a point not on the linetest (0,0)0 -3(0) + 2

Not true!

Graph y -3x + 2 on the coordinate plane.xy

Instead of testing a pointIf in y = mx + b form...Shade upShadedownSolid lineDashed line

> -3x + 12-4 -4y < x - 3

m = b = -3

Boundary LinexyRemember that when you multiply or divide by a negative number..FLIP THE INEQUALITY SIGN!!Example:6425STEP 3

STEP 1STEP 2

Graphing a Linear InequalitySketch a graph of y 3Graphing an Inequality in Two VariablesGraph x < 2Step 1: Start by graphing the line x = 2Now what points would give you less than 2?Since it has to be x < 2 we shade everything to the left of the line.HOMEWORKComplete the kuta worksheet

Surfing with InequalitiesWill the inequality surf splash over our surfer?Decide if the shading of inequality (the surf) will splash over the surfer.

2y > 10-x

7.5 Practice Graph each inequality.Determine if the given point is a solution.Do # 1-3Check solution with your neighbor

Example:

STEP 1STEP 2STEP 3CLASSWORKComplete the surfing with inequalities wshtTurn in for a graded classwork assignmentBe accurate with your graphingBe careful when dividing by a negative #

Absent Student LetterWrite a letter to an absent student explaining what an inequality is and how to graph a system of inequalities?

Graphing ReviewUse a graph to solve each system of equations. a) y = x + 1 and y = -x + 3b) 2x y = 6 and y = x - 2

The solution to a system of Equations is the POINT of INTERSECTION

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