advertisement

A.REI.12 Graphing linear inequalities Name: _______________________ Activator Is the Point a Solution? Directions: 1) On the coordinate plane below, graph the line x – 2y = 8. 2) Determine if each of the given points is a solution of the inequality x – 2y < 8 by substituting the x- and y-coordinates into the inequality. a. If it is a solution, plot a Y for “yes” at the given coordinates. b. If it is not a solution, plot an N for “no” at the given coordinates. 3) Answer the questions that follow. Split this work with your table partners to speed it up! (0, 0) (-6, -7) (0, -5) (4, -6) (3, 3) (8, 0) (-3, -9) (-4, 2) (1, -6) (9, -2) (-4, -6) (0, 6) (5, -3) (-8, -4) (-8, -10) (8, 8) Questions: 1) What do you notice about where the Ys and Ns are? 2) Why is x – 2y = 8 called a “boundary line”? 3) How would this picture change if the inequality had been x – 2y < 8 instead of x – 2y < 8? Support - A.REI.12 **Guided notes organizer on pages 6 & 7 ** Name: _______________________ Practice Graphing Linear Inequalities 1) Determine if each point is a solution to the inequality 3x – 4y > 8 by using the graph shown. a) (3, -4) b) (4, 1) c) (-3, -4) d) (0, 0) e) (-4, -5) f) (1, -10) g) (-1.5, -5) 2) Check your answers to problem 1 algebraically. a) (3, -4) b) (4, 1) c) (-3, -4) d) (0, 0) e) (-4, -5) f) (1, -10) g) (-1.5, -5) 3) Graph each inequality. Pay attention to the type of boundary line you need. a) y > -2.5 b) x < -2.5 c) |y| < 1 d) |x| > 1 e) 5y – 2x < 9 f) y > -2½ – ¾x g) y < -4x + 3 h) 10x – 8y > 24 On Target - A.REI.12 Name: _______________________ Graphing Linear Inequalities 1) Determine whether each point is a solution to the inequality that is shown in the graph to the right. a) (1, 2) b) (4, 3) c) (2, -2) d) (-4, 0) e) (3.27, -4.03) f) (0, -3) g) (10, -5) h) (0, -5) 2) Given the inequality 4x + 5y > 12, determine algebraically if each point is a solution or not. a. (-2, 4) b. (3, -2) c. (0, 2) d. (2, 5) 3) Graph the inequality from problem 2 on the coordinate plane to the right. Use the intercepts method to make the graph. 4) Use the graph to check if your answers to problem 2 are correct. 5) Use the graph to determine if these points are solutions to 4x + 5y > 12: a. (3.7, 2.15) b. (-2, 4.88) c. (5.6, -3.99) d. (0, 0) 6) Graph each inequality. Pay attention to the type of boundary line you need. a) y < 3.5 b) x > -2.5 c) |x| > 2 d) |y| < 4 e) y > -4 – 2x f) -2x – 4y > 10 Extension Graph: 1) y < (x – 2)2 – 3 2) y > |x + 2| – 2 Lesson Name: Linear Inequalities Date: _________________ Student: ___________________________ Support Notes: Systems Concepts Examples y4 x 1 y 3 of Equations and Inequalities Background Information Concepts Examples x 4 y 2x 3 4x 5y 10 Background Information