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**Graphing a Linear Inequality**

So far, we have been graphing linear equality lines (i.e. y = 2x + 1) Now let’s look at graphing linear inequality lines (i.e. y > 2x + 1) Graphing a linear inequality is very similar to graphing a linear equality.

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**Graphing a Linear Inequality**

Step 1) Solve the inequality for y (or for x if there is no y). Step 2) Change the inequality to an equation and graph like before Step 3) If the inequality is < or > (not equals), the line is dashed ( ). If the inequality is ≤ or ≥, the line is solid (______). Step 4) If the inequality is < or ≤, you shade below or to the left of the line. If the inequality is > or ≥, you shade above or to the right of the line.

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**Graph: y- 2x ≤ + 1 Step 1: Solve the inequality for y: y ≤ 2x+1**

Step 2: Graph the line y = 2x + 1 Step 3: Because y ≤ 2x+1 and not <, the line will be solid Step 4: Now shade the side of the line where y < 2x+1 (below the line).

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**Graph -y – x < 2 Step 1: Solve the inequality for y: y > -x – 2**

Step 2: Graph the equality y = -x – 2 Step 3: Because y > -x – 2 and not ≥, the line will be dotted Step 4: Now shade the side of the line where y > -x - 2 (above the line).

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**Graph the inequality 3 – x > 0**

Step 1: Solve the inequality for x 3 - x > 0 -x > -3 x < 3

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**Graph: x < 3 Step 2: Graph the line x = 3 Step 3: Because x < 3,**

the line will be dotted Step 4: Now shade the side of the line where x < 3 (to the left of the line) 6 4 2 3

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**Check if your graph is correct**

To check that the shading is correct, pick a point in the area and plug it into the inequality. If the inequality statement is true, the shading is correct. If the inequality statement is false, the shading is incorrect.

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**Check if your graph is correct**

Pick a point, (1,2), in the shaded area. Substitute into the original inequality 3 – x > 0 3 – 1 > 0 2 > 0 True! The inequality has been graphed correctly. 6 4 2 3

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**Given the inequality graphed below:**

a.) Write an inequality statement. b.) Name one ordered pair that is not in the solution set. c.) Name one ordered pair that is in the solution set.

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**Given the inequality graphed below:**

a.) Write an inequality statement. b.) Name one ordered pair that is not in the solution set. c.) Name one ordered pair that is in the solution set.

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**Write a system of inequalities for the dark blue solution shown on the graph below.**

(Hint: you should write 2 different inequalities – one for each graph)

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**Write a system of inequalities for the green solution shown on the graph below.**

(Hint: you should write 2 different inequalities – one for each graph)

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**Write a system of inequalities for the dark blue solution shown on the graph below.**

(Hint: you should write 2 different inequalities – one for each graph)

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**Write a system of inequalities for the dark blue solution shown on the graph below.**

(Hint: you should write 2 different inequalities – one for each graph)

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**Write a system of inequalities for the blue solution shown on the graph below.**

(Hint: you should write 3 different inequalities – one for each graph)

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