Graphing Inequalities inin Graphing Inequalities 11 6 Two

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Graphing Inequalities inin Graphing Inequalities 11 -6 Two Variables Warm Up Problem of the

Graphing Inequalities inin Graphing Inequalities 11 -6 Two Variables Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Warm Up Find each equation of direct

Graphing Inequalities in 11 -6 Two Variables Warm Up Find each equation of direct variation, given that y varies directly with x. y = 6 x 1 x y = 2. x is 60 when y is 12. 5 3. y is 126 when x is 18. y = 7 x 1. y is 18 when x is 3. 4. x is 4 when y is 20. Pre-Algebra y = 5 x

Graphing Inequalities in 11 -6 Two Variables Problem of the Day The circumference of

Graphing Inequalities in 11 -6 Two Variables Problem of the Day The circumference of a pizza varies directly with its diameter. If you graph that direct variation, what will the slope be? Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Today’s Learning Goal Assignment Learn to graph

Graphing Inequalities in 11 -6 Two Variables Today’s Learning Goal Assignment Learn to graph inequalities on the coordinate plane. Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Vocabulary boundary linear inequality Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Vocabulary boundary linear inequality Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables A graph of a linear equation separates

Graphing Inequalities in 11 -6 Two Variables A graph of a linear equation separates the coordinate plane into three parts: the points on one side of the line, the points on the boundary line, and the points on the other side of the line. Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables When the equality symbol is replaced in

Graphing Inequalities in 11 -6 Two Variables When the equality symbol is replaced in a linear equation by an inequality symbol, the statement is a linear inequality. Any ordered pair that makes the linear inequality true is a solution. Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 A: Graphing Inequalities Graph

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 A: Graphing Inequalities Graph each inequality. A. y < x – 1 First graph the boundary line y = x – 1. Since no points that are on the line are solutions of y < x – 1, make the line dashed. Then determine on which side of the line the solutions lie. (0, 0) Test a point not on the line. y<x– 1 ? 0<0– 1 ? 0 < – 1 Pre-Algebra Substitute 0 for x and 0 for y.

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 A Continued Since 0

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 A Continued Since 0 < – 1 is not true, (0, 0) is not a solution of y < x – 1. Shade the side of the line that does not include (0, 0). Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 A Graph each

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 A Graph each inequality. A. y < x – 4 First graph the boundary line y = x – 4. Since no points that are on the line are solutions of y < x – 4, make the line dashed. Then determine on which side of the line the solutions lie. (0, 0) Test a point not on the line. y<x– 4 ? 0<0– 4 ? 0 < – 4 Pre-Algebra Substitute 0 for x and 0 for y.

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 A Continued Since

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 A Continued Since 0 < – 4 is not true, (0, 0) is not a solution of y < x – 4. Shade the side of the line that does not include (0, 0). Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 B: Graphing Inequalities B.

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 B: Graphing Inequalities B. y 2 x + 1 First graph the boundary line y = 2 x + 1. Since points that are on the line are solutions of y 2 x + 1, make the line solid. Then shade the part of the coordinate plane in which the rest of the solutions of y 2 x + 1 lie. (0, 4) Choose any point not on the line. y ≥ 2 x + 1 ? 4≥ 0+1 Pre-Algebra Substitute 0 for x and 4 for y.

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 B Continued Since 4

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 B Continued Since 4 1 is true, (0, 4) is a solution of y 2 x + 1. Shade the side of the line that includes (0, 4). Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 B B. y

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 B B. y > 4 x + 4 First graph the boundary line y = 4 x + 4. Since points that are on the line are solutions of y 4 x + 4, make the line solid. Then shade the part of the coordinate plane in which the rest of the solutions of y 4 x + 4 lie. (2, 3) Choose any point not on the line. y ≥ 4 x + 4 ? 3≥ 8+4 Pre-Algebra Substitute 2 for x and 3 for y.

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 B Continued Since

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 B Continued Since 3 12 is not true, (2, 3) is not a solution of y 4 x + 4. Shade the side of the line that does not include (2, 3). Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 C: Graphing Inequalities C.

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 C: Graphing Inequalities C. 2 y + 5 x < 6 First write the equation in slope-intercept form. 2 y + 5 x < 6 2 y < – 5 x + 6 y < – 5 x + 3 2 Subtract 5 x from both sides. Divide both sides by 2. Then graph the line y = – 5 x + 3. Since points that 2 are on the line are not solutions of y < – 5 x + 3, 2 make the line dashed. Then determine on which side of the line the solutions lie. Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 C Continued (0, 0)

Graphing Inequalities in 11 -6 Two Variables Additional Example 1 C Continued (0, 0) 5 y < – 2 x + 3 ? 0<0+3 Choose any point not on the line. ? 0<3 Since 0 < 3 is true, (0, 0) is a 5 solution of y < – 2 x + 3. Shade the side of the line that includes (0, 0). Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 C C. 3

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 C C. 3 y + 4 x 9 First write the equation in slope-intercept form. 3 y + 4 x 9 3 y – 4 x + 9 y – 4 x + 3 3 Subtract 4 x from both sides. Divide both sides by 3. Then graph the line y = – 4 x + 3. Since points that 3 are on the line are solutions of y – 4 x + 3, make 3 the line solid. Then determine on which side of the line the solutions lie. Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 C Continued (0,

Graphing Inequalities in 11 -6 Two Variables Try This: Example 1 C Continued (0, 0) y – 4 x + 3 3 ? 0 0+3 Choose any point not on the line. ? 0 3 Since 0 3 is not true, (0, 0) is not a solution of y – 4 x + 3. 3 Shade the side of the line that does not include (0, 0). Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Lesson Quiz Graph each inequality. 1 1.

Graphing Inequalities in 11 -6 Two Variables Lesson Quiz Graph each inequality. 1 1. y < – 3 x + 4 2. 4 y + 2 x > 12 Tell whether the given ordered pair is a solution of each inequality. 3. y < x + 15 (– 2, 8) 4. y 3 x – 1 (7, – 1) Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables 1. y < – 1 x +

Graphing Inequalities in 11 -6 Two Variables 1. y < – 1 x + 4 3 Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables 2. 4 y + 2 x >

Graphing Inequalities in 11 -6 Two Variables 2. 4 y + 2 x > 12 Pre-Algebra

Graphing Inequalities in 11 -6 Two Variables Tell whether the given ordered pair is

Graphing Inequalities in 11 -6 Two Variables Tell whether the given ordered pair is a solution of each inequality. 3. y < x + 15 (– 2, 8) yes 4. y 3 x – 1 (7, – 1) Pre-Algebra no