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**Graphing Linear Inequalities in Two Variables**

Objective: Graph all of the solutions to a linear inequality NCSCOS: 1.02, 3.03, 4.01

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Steps to Remember Rewrite the inequality so that it is in slope-intercept form y = mx + b Plot the y-intercept (b) Use the slope (m) to find other points on the line. Draw the line Solid if <= or >= Dotted if < or > Shade above or below the line Above if > or >= Below if < or <=

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Example 1 Graph y > 2x -5 The equation is already in slope-intercept form. Start by plotting the y-intercept (b = -5)

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**Example 1 (cont) Graph y > 2x -5**

Now use the slope to find other points on the line

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**Example 1 (cont) Graph y > 2x -5**

Draw a dotted or solid line through the coordinates. This line will be dotted since the inequality is >

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**Example 1 (cont) Graph y > 2x -5**

Shade above the line to show all of the coordinates that are solutions.

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**Example 2 Graph 2x - 5y >=15 First, solve for y …**

-5y >= -2x + 15 y <= 2/5 x – 3 Now go through the steps of graphing.

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Example 2 Graph 2x - 5y >=15 y <= 2/5 x – 3 Plot the y-intercept

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**Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3**

Use the slope to find other points

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**Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3**

Draw a solid line through the points.

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Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3 Shade below the line

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**Special Example Graph x > 5**

Remember the graph will be a vertical line.

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**Special Example Graph y< -2**

Remember the graph will be a horizontal line.

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. Solve the inequality. Then graph the solution. 9 ≤ + – 4x 7 12x 1.

. Solve the inequality. Then graph the solution. 9 ≤ + – 4x 7 12x 1.

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