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Published bySebastian Manning Modified over 3 years ago

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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 1. Rewrite the inequality so that it is in slope-intercept form y = mx + b y = mx + b 2. Plot the y-intercept (b) 3. Use the slope (m) to find other points on the line. 4. Draw the line Solid if = Solid if = Dotted if Dotted if 5. Shade above or below the line Above if > or >= Above if > or >= Below 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 Graph x > 5 Remember the graph will be a vertical line. Remember the graph will be a vertical line.

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Special Example Graph y< -2 Graph y< -2 Remember the graph will be a horizontal line. Remember the graph will be a horizontal line.

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