Objectives: Students will write, solve, and graph linear inequalities with one and two variables. Warm-up: (Get a sheet of graph paper from the back of the room.) Find the x and y intercepts for this inequality: y + 3x > 4 x-intercept: set y = 0 and solve for x y-intercept: set x = 0 and solve for y Find the slope for this line. (y = mx + b, where m = slope and b = y-intercept) Using a complete sentence, explain how you would draw this line on a graph. (There are at least three right answers.) Graphing inequalities. Step 1: Graph the boundary line. Solid boundary line: < or > Dashed boundary line: < or > Step 2: Plug in a test point that is not on the boundary line. Step 3: Shade in the answer to the inequality. Practice: y ≥ (1/2) x - 1 Step 1: Graph the boundary line. You can use: 1) Slope intercept: y ≥ (1/2) x - 1 y = mx + b, where m = slope and b = y-intercept y ≥ (1/2) x - 1, slope = 1/2 and y-intercept = -1 Therefore, plot (0, -1) and then draw a line with slope = 1/2 or 2) Find x and y intercepts. How? Set y = 0 and solve for x: y ≥ (1/2) x - 1 0 = (1/2)x - 1 1 = (1/2)x 2=x Therefore, (2, 0) and Set x = 0 and solve for y: y ≥ (1/2) x - 1 y = (1/2)(0) - 1, y = -1 Therefore, (0, 1) Solid boundary line: < or > Dashed boundary line: < or > Step 2: Plug in a test point that is not on the boundary line. Any number will do, but (0,0) usually works. y ≥ (1/2) x - 1 0 ?≥? (1/2) (0) - 1 0 ?≥? - 1 --> Yes! Step 3: Shade in the answer to the inequality. Which side of the line is (0,0) on? Practice: y ≤ 2x - 5 Step 1: Graph the boundary line. Step 2: Plug in a test point that is not on the boundary line. Step 3: Shade in the answer to the inequality. Inequality Quiz. 1. 2. 3. 4. Open notes 30 minutes Show all of your work