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Published bySebastian Manning Modified over 4 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 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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Notes Over 2.6 Checking Solutions of Inequalities Check whether the given ordered pairs are solutions of the inequality.

Notes Over 2.6 Checking Solutions of Inequalities Check whether the given ordered pairs are solutions of the inequality.

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