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**Graphing Linear Inequalities in Two Variables**

graph a linear inequality in two variables model a real life situation with a linear inequality.

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Recall… Graph n < 3 on a number line.

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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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**Graph x -2 on the coordinate plane.**

y x

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**Graph y > 3 on the coordinate plane.**

x

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**Graphing a Linear Inequality**

Sketch a graph of y 3

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**Some Helpful Hints If the sign is > or < the line is dashed**

If the sign is or the line will be solid When dealing with just x and y. If the sign > or the shading either goes up or to the right If the sign is < or the shading either goes down or to the left

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

y < x - 3 x Boundary Line m = b = -3

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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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Problem If you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have. Let n = # of nickels Let d = # of dimes 0.05 n d < 5.00 or 5 n + 10 d < 500

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5n + 10d < 500 n d d 50 60 50 40 30 20 10 100 n

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**Graphing Absolute Value Inequalities**

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**Graphing Absolute Value Inequalities**

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