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Graphing Linear Inequalities in Two Variables LESSON ESSENTIAL QUESTION: How do you graph an inequality? WARMUP Complete Day 4 Warmup Problems Shade, Shade, Shade, Shade It • http://teachertube.com/viewVideo.php?video _id=121267 Put the equations into y=mx+b form to graph! Graphing Review Graph each line. a) y = x + 2 b) x – 2y = 6 Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation. Graphing Inequalities Where do you think the points that are y > x + 2 are located? Where do you think the points that are y < x + 2 are located? Graphing Inequalities The line is the boundary of the two regions. The blue region is the “greater than” (>) area and the yellow region is the “less than” (<) area. YOU WERE RIGHT!! Graphing Inequalities When the line that represents y = x + 2 is solid, not dashed, it means that the points on the line are included in the inequality. So we would state that the blue are can be represented by y x + 2. And, the yellow could be represented by y x + 2. Graphing Inequalities When the line that represents y = x + 2 is dashed, it means that the points on the line are not included in the inequality. So we would state that the blue are can be represented by y > x + 2. And, the yellow could be represented by y < x + 2. Tell Your Neighbor • What does it mean to be a point in the solution of an inequality? – A point in the shaded area of the solution set that fits the inequality • Name 1 point in the solution set • Name 1 point NOT in the solution set Steps to Graphing Linear Inequalities 1. Change the inequality into slope-intercept form, y = mx + b. Graph the equation. 2. If > or < then the line should be dashed. If > or < then the line should be solid. 3. If y > mx+b or y > mx+b, shade above the line. If y < mx+b or y < mx+b, shade below the line. 4. To check that the shading is correct, pick a point in the area and plug it into the inequality – – If TRUE, you shaded correct If FALSE, you shaded incorrectly GRAPHING INEQUALITIES INEQUALITY SYMBOL TYPE OF LINE (dashed or solid) WHERE TO SHADE < > ≤ ≥ dashed below dashed above solid below solid above (above or below line) GRAPHING INEQUALITIES SOLID LINE DASHED LINE SHADE UP SHADE BELOW ≥ ≤ > < When dealing with slanted lines •If it is > or then you shade above •If it is < or then you shade below the line Graph y -3x + 2 on the coordinate plane. y Boundary Line - y = 3x + 2 - m= 3 3 1 b=2 x Test a point not on the line test (0,0) 0 -3(0) + 2 Not true! Graph y -3x + 2 on the coordinate plane. y Instead of testing a point If in y = mx + b form... Shade up Solid line Dashed line > Shade down < x Surfing with Inequalities • Will the inequality “surf” splash over our surfer? • Step 1: Graph line • Step 2: Dashed or solid line? • Step 3: Shade above or below line? • Step 4: Verify a point y ≥ 2x Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y <-x + 3 Step 2: Graph the line y = -x + 3 STEP 1 Example: 2 y x4 3 1. 2x 3y 12 6 STEP 3 4 STEP 2 2 5 Graph on the coordinate plane. 3x - 4y > 12 -3x -3x -4y > -3x + 12 -4 -4 3 y < x-3 4 Boundary Line 3 m= 4 b = -3 y Remember that when you multiply or divide by a negative number..FLIP THE INEQUALITY SIGN!! x STEP 1 Example: 2. x 3 y > 6 6 STEP 2 4 STEP 3 2 5 1 y< x2 3 Graphing a Linear Inequality Sketch a graph of y 3 Graphing an Inequality in Two Variables Graph x < 2 Step 1: Start by graphing the line x = 2 Now what points would give you less than 2? Since it has to be x < 2 we shade everything to the left of the line. HOMEWORK • Complete the kuta worksheet Surfing with Inequalities • Will the inequality “surf” splash over our surfer? • Decide if the shading of inequality (the surf) will splash over the surfer. 2y > 10-x 7.5 Practice • • • • Graph each inequality. Determine if the given point is a solution. Do # 1-3 Check solution with your neighbor Example: 3. x 1 STEP 1 6 STEP 2 4 STEP 3 2 -5 5 -2 CLASSWORK • Complete the surfing with inequalities wsht • Turn in for a graded classwork assignment • Be accurate with your graphing • Be careful when dividing by a negative # Absent Student Letter • Write a letter to an absent student explaining what an inequality is and how to graph a system of inequalities? The solution to a system of Equations is the POINT of INTERSECTION Graphing Review Use a graph to solve each system of equations. a) y = x + 1 and y = -x + 3 b) 2x – y = 6 and y = x - 2