Name _____________________________ Unit 3 – Graphing 11-28-16 Date ____________ Math 8 Aim #40: How do we graph linear inequalities in two variables? HW #40: Graphing Linear Inequalities Handout Do Now: Write the equation of the line passing through the points (9, -3) and (5, -11). Graphing Linear Inequalities Example: a) Graph the equation y = 3x + 5. b) Does changing the equation y = 3x + 5 to the inequality y ≥ 3x + 5 change the solution set of the graph? Show examples to support your answer. c) Now represent y ≥ 3x + 5 on the graph below. d) How would the graph from part c be different if we change y ≥ 3x + 5 to y > 3x + 5? Represent y > 3x + 5 on the graph. 1) a) Graph y - 2x ≤ 3. Step 1: Solve the inequality for ____ first! Step 2: Graph the inequality just like you graph a linear equation by identifying the ________ and ___________. Step 3: Connect the points to form the __________ line. Step 4: Choose a ______ point to determine which side of the boundary line to shade for the solution set. Step 5: Label the graph with the __________ inequality. a) Is (5, 1) a solution to the inequality? b) Is (-7, 4) a solution to the inequality? The solution of an inequality are the coordinates on the region of a graph that make the inequality true. 1) Boundary Line: a) ≤ or ≥ b) < or > solid line dashed line 2) Shading: Substitute a test point into the original inequality. If the inequality is true, shade the region with the test point If the inequality is false, shade the region without the test point What would be the easiest test point to use? When can you not use your answer from the previous question as a test point? Graph each inequality. 2) 3x - 5y < 10 3) x + 3y ≤ -6 4) x < 2 5) y ≥ -5 6) y - 5 < 3(x + 1) Circle the ordered pairs that are solutions to the inequality 4x - y ≤ 10. (2, 3) (6, 0) (4, -1) (1, -6) (-2, -18) Summmary: We use a ___________ line when graphing the inequalities < or >. We use a ___________ line when graphing the inequalities ≤ or ≥.

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