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**LESSON ESSENTIAL QUESTION:**

Graphing Linear Inequalities in Two Variables LESSON ESSENTIAL QUESTION: How do you graph an inequality?

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WARMUP Complete Day 4 Warmup Problems

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**Shade, Shade, Shade, Shade It**

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

Graphing Review Graph each line. a) y = x b) x – 2y = 6

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**Graphing a Linear Inequality**

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

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**Graphing Inequalities**

Where 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?

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**Graphing Inequalities**

The line is the boundary of the two regions. The blue region is the “greater than” (>) area and the yellow region is the “less than” (<) area. YOU WERE RIGHT!!

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**Graphing Inequalities**

When the line that represents y = x + 2 is solid, not dashed, it means that the points on the line are included in the inequality. So we would state that the blue are can be represented by y ³ x + 2. And, the yellow could be represented by y £ x + 2.

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**Graphing Inequalities**

When the line that represents y = x + 2 is dashed, it means that the points on the line are not included in the inequality. So we would state that the blue are can be represented by y > x And, the yellow could be represented by y < x + 2.

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Tell Your Neighbor What 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 inequality Name 1 point in the solution set Name 1 point NOT in the solution set

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**Steps to Graphing Linear Inequalities**

1. 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 inequality If TRUE, you shaded correct If FALSE, you shaded incorrectly

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**GRAPHING INEQUALITIES**

INEQUALITY SYMBOL TYPE OF LINE (dashed or solid) WHERE TO SHADE (above or below line) < > ≤ ≥ dashed below dashed above solid below solid above

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**GRAPHING INEQUALITIES**

SHADE UP SHADE BELOW SOLID LINE DASHED LINE ≥ ≤ > <

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**When dealing with slanted lines**

If it is > or then you shade above If it is < or then you shade below the line

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

Boundary Line y = -3x + 2 m = -3 b = 2 x Test a point not on the line test (0,0) (0) + 2 Not true!

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**> < Graph y -3x + 2 on the coordinate plane. y**

Instead of testing a point If in y = mx + b form... Shade up Shade down Solid line x > < Dashed line

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**Surfing with Inequalities**

y ≥ 2x Will the inequality “surf” splash over our surfer? Step 1: Graph line Step 2: Dashed or solid line? Step 3: Shade above or below line? Step 4: Verify a point

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**Step 1: Put into slope intercept form**

Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y <-x + 3 Step 2: Graph the line y = -x + 3

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STEP 1 Example: STEP 3 STEP 2 6 4 2 5

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**-3x -3x -4y > -3x + 12 -4 -4 Graph on the coordinate plane.**

Remember that when you multiply or divide by a negative number..FLIP THE INEQUALITY SIGN!! 3x - 4y > 12 y -3x x -4y > -3x + 12 y < x - 3 x Boundary Line m = b = -3

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STEP 1 Example: 6 4 2 5 STEP 2 STEP 3

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**Graphing a Linear Inequality**

Sketch a graph of y 3

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**Graphing an Inequality in Two Variables**

Graph x < 2 Step 1: Start by graphing the line x = 2 Now what points would give you less than 2? Since it has to be x < 2 we shade everything to the left of the line.

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HOMEWORK Complete the kuta worksheet

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**Surfing with Inequalities**

Will the inequality “surf” splash over our surfer? Decide if the shading of inequality (the surf) will splash over the surfer. 2y > 10-x

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**7.5 Practice Graph each inequality.**

Determine if the given point is a solution. Do # 1-3 Check solution with your neighbor

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Example: STEP 1 STEP 2 STEP 3

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**CLASSWORK Complete the surfing with inequalities wsht**

Turn in for a graded classwork assignment Be accurate with your graphing Be careful when dividing by a negative #

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

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

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

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