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Graphing Linear Inequalities in Two Variables

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!.

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Graphing Linear Inequalities in Two Variables

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  1. Graphing Linear Inequalities in Two Variables LESSON ESSENTIAL QUESTION: How do you graph an inequality?

  2. WARMUP Complete Day 4 Warmup Problems

  3. Shade, Shade, Shade, Shade It • http://teachertube.com/viewVideo.php?video_id=121267

  4. Put the equations into y=mx+b form to graph! Graphing Review Graph each line. a) y = x + 2 b) x – 2y = 6

  5. Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

  6. 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?

  7. 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!!

  8. 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 byy ³ x + 2. And, the yellow couldbe represented by y £ x + 2.

  9. 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.

  10. 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

  11. 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, shadeabove the line. If y < mx+b or y <mx+b, shade belowthe line. • 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

  12. GRAPHING INEQUALITIES below dashed above dashed below solid above solid

  13. GRAPHING INEQUALITIES ≥ ≤ > <

  14. When dealing with slanted lines • If it is > or  then you shade above • If it is < or  then you shade below the line

  15. Graph y -3x + 2 on the coordinate plane. y Boundary Line y =-3x + 2 m =-3 b = 2 x Test a point not on the line test (0,0) 0 -3(0) + 2 Not true!

  16. Graph y -3x + 2 on the coordinate plane. y Instead of testing a point If in y = mx + b form... Shade up Shade down Solid line x > < Dashed line

  17. Surfing with Inequalities y ≥ 2x • 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

  18. 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

  19. STEP 1 6 STEP 3 4 STEP 2 2 5 Example:

  20. Graph on the coordinate plane. Remember that when you multiply or divide by a negative number..FLIP THE INEQUALITY SIGN!! 3x - 4y > 12 y -3x -3x -4y >-3x + 12 -4 -4 y < x - 3 x Boundary Line m = b =-3

  21. STEP 1 6 4 STEP 3 2 5 Example: STEP 2

  22. Graphing a Linear Inequality Sketch a graph of y  3

  23. 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.

  24. HOMEWORK • Complete the kuta worksheet

  25. 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

  26. 7.5 Practice • Graph each inequality. • Determine if the given point is a solution. • Do # 1-3 • Check solution with your neighbor

  27. Example: STEP 1 STEP 2 STEP 3

  28. 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 #

  29. Absent Student Letter • Write a letter to an absent student explaining what an inequality is and how to graph a system of inequalities?

  30. 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

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