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Do Now 1/6/10 Take out HW from last night. –Text p. 401, #4-20 multiples of 4 & #22, 26, & 28 Copy HW in your planner. –Text p. 409, #4-52 multiples of 4. –Chapter 6 Test Friday In your notebook, explain how to graph the following line; y = 4x – 3 In your notebook, explain how to graph the following line; y = 4x – 3

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Homework Text p. 401, #4-20 multiples of 4; #22, 26, & 28 4) y ≤ -3 or y ≥ 3 8) j ≤ -1¾ or y ≥ 1¾ 12) 3 < s < 4 16) s 13½ 20) f ≤ -12 or y ≥ 9 22) AND is for, ≥ 26) |2x + 7| ≥ 15; x ≤ -11 or x ≥ 4 28) 4|x – 9| < 8; 7 < x < 11

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Objective SWBAT graph linear equations and linear inequalities in two variables

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Section 6.7 “Graph Linear Inequalities” Section 6.7 “Graph Linear Inequalities” Linear Inequalities- the result of replacing the = sign the result of replacing the = sign in a linear equation with an inequality sign.

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Linear Inequalities An example of a linear inequality in two variables is x - 3y ≤ 6. The solution of an inequality in two variables, x and y, is an ordered pair (x, y) that produces a true statement when substituted into the inequality. Which ordered pair is NOT a solution of x - 3y ≤ 6? A. (0,0) B. (6,-1) C. (10, 3) D. (-1,2) x - 3y ≤ 6 Substitute each point into the inequality. If the statement is true then it is a solution. (0) – 3(0) ≤ 6 True, therefore (0,0) is a solution.

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The graph of an inequality in two variables is the set of points that represent all solutions of the inequality. The BOUNDARY LINE of a linear inequality divides the coordinate plane into two HALF-PLANES. Only one half-plane contains the points that represent the solutions to the inequality. Graph an Inequality in Two Variables

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Graphing Linear Inequalities Graphing Boundary Lines: –Use a dashed line for. –Use a solid line for ≤ or ≥.

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Graph an Inequality Graph the equation STEP 1 Graph the inequality y > 4x - 3. STEP 2 Test (0,0) in the original inequality. STEP 3 Shade the half-plane that contains the point (0,0), because (0,0) is a solution to the inequality.

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Graph an Inequality Graph the equation STEP 1 Graph the inequality. Graph the inequality x + 2y ≤ 0. STEP 2 Test (1,0) in the original inequality. STEP 3 Shade the half-plane that does not contain the point (1,0), because (1,0) is not a solution to the inequality.

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Graph an Inequality Graph the equation STEP 1 Graph the inequality. Graph the inequality x + 3y ≥ -1. STEP 2 Test (1,0) in the original inequality. STEP 3 Shade the half-plane that contains the point (1,0), because (1,0) is a solution to the inequality.

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Graph an Inequality Graph the equation STEP 1 Graph the inequality. Graph the inequality y ≥ -3. STEP 2 Test (2,0) in the original inequality. Use only the y- coordinate, because the inequality does not have a x-variable. STEP 3 Shade the half-plane that contains the point (2,0), because (2,0) is a solution to the inequality.

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Graph an Inequality Graph the equation STEP 1 Graph the inequality x. Graph the inequality x ≤ -1. STEP 2 Test (3,0) in the original inequality. Use only the y- coordinate, because the inequality does not have a x-variable. STEP 3 Shade the half-plane that does not contain the point (3,0), because (3,0) is not a solution to the inequality.

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Challenge “Can You Write and Graph the Mystery Inequality???” The points (2,5) and (-3, -5) lie on the boundary line. The points (6,5) and (-2, -3) are solutions of the inequality. y ≤ 2x + 1

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ABSOLUTE VALUE FUNCTION- Graph Absolute Value Functions Extension Activity 6.5 xf(x)=|x| -55 -22 00 11 33 f(x) = |x| g(x) = |x -3|xg(x)=|x-3|-36 03 30 41 63

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Read pages 396-397. Complete #1-7 on page 397. Make sure to graph and compare each function to f(x) = |x|. Graph Absolute Value Functions Extension Activity 6.5

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Homework Text p. 409, #4-52 multiples of 4 Text p. 409, #4-52 multiples of 4

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Graphing Inequalities of Two Variables Recall… Solving inequalities of 1 variable: x + 4 ≥ 6 x ≥ 2 [all points greater than or equal to 2] Different from.

Graphing Inequalities of Two Variables Recall… Solving inequalities of 1 variable: x + 4 ≥ 6 x ≥ 2 [all points greater than or equal to 2] Different from.

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