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Graphing Linear Inequalities in Two Variables

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Linear Inequalities A linear inequality in two variables can be written in any one of these forms: Ax + By < C Ax + By > C Ax + By ≤ C Ax + By ≥ C An ordered pair (x, y) is a solution of the linear inequality if the inequality is TRUE when x and y are substituted into the inequality.

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Example 1 Which ordered pair is a solution of 5x - 2y ≤ 6? A.(0, -3) B.(5, 5) C.(1, -2) D.(3, 3)

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The boundary line will be a: – Solid line when ≤ and ≥ are used. – Dashed line when are used. shaded Graph will be shaded on one side of the boundary line to show the solutions. Graphing LinearInequalities

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STEPS: 1.Graph the boundary line: ≤ and ≥ will use a solid curve. will use a dashed curve. 2.Test a point NOT on the boundary line to determine which side of the line includes the solutions. If your test point is a solution, shade that side. If your test points is NOT a solution, shade the opposite side. Graphing LinearInequalities

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Example 2 Graph the inequality x ≤ 4 in a coordinate plane. HINT: – Decide whether to use a solid or dashed line. Use (0, 0) as a test point. Shade where the solutions will be. y x 5 5 -5

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Example 3 Graph 3x - 4y > 12 in a coordinate plane. Sketch the boundary line of the graph. – Find the x- and y-intercepts and plot them. – Solid or dashed line? Use (0, 0) as a test point. Shade where the solutions are. y x 5 5 -5

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Example 4: Using a new Test Point Graph y < 2 / 5 x in a coordinate plane. Sketch the boundary line of the graph. Find the x- and y-intercept and plot them. Use the line’s slope to graph another point. – Solid or dashed line? Use a test point OTHER than the origin. Shade where the solutions are. y x 5 5 -5

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Example 5: Let’s Try This! Graph y ≥ 3x + 1 in a coordinate plane. y x

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Example 6: You Try Graph y + 2x < 4 in a coordinate plane. y x

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Example 7: You Try Graph 2x – 3y ≤ 6 in a coordinate plane. y x

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Example 8: You Try Graph 2y > x in a coordinate plane. y x

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Homework Inequality Worksheet Inequality Worksheet – SHOW WORK! – SHOW WORK! – GRAPH! – GRAPH!

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