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EXAMPLE 2 Graph linear inequalities with one variable Graph (a) y < –3 and (b) x < 2 in a coordinate plane. a. Graph the boundary line y = –3. Use a solid line because the inequality symbol is < . Test the point (0,0). Because (0,0) is not a solution of the inequality, shade the half- plane that does not contain (0,0).

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EXAMPLE 2 Graph linear inequalities with one variable b. Graph the boundary line x = 2.Use a dashed line because the inequality symbol is < . Test the point (0,0). Because (0,0) is a solution of the inequality, shade the half-plane that does not contains (0,0).

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EXAMPLE 3 Graph linear inequalities with two variables Graph (a) y > –2x and (b) 5x – 2y ≤ –4 in a coordinate plane. a. Graph the boundary line y = –2x. Use a dashed line because the inequality symbol is >. Test the point (1,1). Because (1,1) is a solution of the inequality, shade the half-plane that contains (1,1).

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EXAMPLE 3 Graph linear inequalities with two variables b. Graph the boundary line 5x –2y = –4.Use a solid line because the inequality symbol is < . Test the point (0,0). Because (0,0) is not a solution of the inequality, shade the half-plane that does not contain (0,0).

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**Shade to the numbers greater than –1 Do not forget dotted line for**

GUIDED PRATICE You try!!! Graph the inequality in a coordinate plane. y > –1 Shade to the numbers greater than –1 Do not forget dotted line for > or < sign y > –1

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GUIDED PRACTICE You try !! Graph the inequality in a coordinate plane. x > –4 x > –4 Shade to the right because the numbers are bigger to the right and the innequality is a greater than or equal to.

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**Already in slope- Intercept form so just use b=0 start at origin**

GUIDED PRACTICE You try !!! Graph the inequality in a coordinate plane. y > –3x y > –3x Already in slope- Intercept form so just use b=0 start at origin slope is –3 down 3 over 1. Solid line.

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GUIDED PRACTICE Try this !!! Graph the inequality in a coordinate plane. y < 2x +3 Y-int. is 3 so start there Then the slope is 2 so up 2 over one. Draw a dotted line because Of the inequality symbol. y < 2x +3

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**First slope intercept form:**

GUIDED PRACTICE Try this !!! Graph the inequality in a coordinate plane. x + 3y < 9 First slope intercept form: x + 3y < 9 Now plot b=3 and use the slope down 1 over 3

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EXAMPLE 1 Standardized Test Practice SOLUTION Ordered pair Substitute Conclusion (6, –3) 3(6) + 4(– 3) = 6 > 8 (6, –3) is not a solution (0, 2) 3(0) + 4(2) = 8 > 8 (0, 2) is not a solution (–2 , –1) is not a solution (–2, –1) 3(–2) + 4(–1) = –10 > 8 (–3, 5) 3(–3) + 4(5) = 11 > 8 (–3, 5) is a solution

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EXAMPLE 1 Standardized Test Practice ANSWER The correct answer is D.

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GUIDED PRACTICE for Example 1 Tell whether the given ordered pair is a solution of 5x – 2y ≤ 6. Ordered pair Conclusion ANSWER (0, –4) (0, – 4 ) is not a solution (2, 2 ) is a solution (2, 2) (–3, 8 ) is a solution (–3, 8) (–1, –7) (– 1, – 7 ) is not a solution

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