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Graphing Linear Inequalities

Graphing Linear Inequalities. February 16, 2010. Last Updated: October 11, 2005. Warm Up. In how many different ways can Larry line up 5 different books on a shelf? a. 1 b. 5 c. 25 d. 120

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Graphing Linear Inequalities

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  1. Graphing Linear Inequalities February 16, 2010 Last Updated: October 11, 2005

  2. Warm Up • In how many different ways can Larry line up 5 different books on a shelf? a. 1 b. 5 c. 25 d. 120 2. Latisha is hosting a wedding in a room that holds 140 people. She has tables that seat 8 people each. What is the GREATEST number of tables she can use in the room? Write an inequality to represent this situation. • How many tables can Latisha use? a. 10 or more tables b. 17 or fewer tables c. 17 or more tables d. Exactly 140 tables

  3. Graphing LinearInequalities slope and y-intercept Jeff Bivin -- LZHS

  4. Graphing Linear Equations • Put the equation in the form of y = mx + b.(Slope Intercept Form) 2. Find b (y-intercept) on the y axis and plot a point. 3. Use m (slope) to find a second and third point. (Use rise/run). 4. Connect the points to form a line.

  5. Graphing Linear Inequalities • Follow the steps for graphing a linear equation, but don’t draw the line. • Decide if the boundary “line” will be open (dashed) or closed (solid). • If it is or , use a solid line. • If it is < or > , use a dashed line. 3. Connect the points with the boundary line. 4. Shade the half plane. • If it is or > , shade the area above the line. • If it is or < , shade the area below the line.

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

  7. y = 2x + 1 y ≤2x + 1 Run 1 y-intercept Rise b = 1 2 slope m = 2 Jeff Bivin -- LZHS

  8. y = 2x + 1 y ≤2x + 1 Now for the shading Pick a point on either side of the graph Let’s try (2, 1) Does the point satisfy the inequality? Shade 1 ≤2(2) + 1 1 ≤4 + 1 TRUE 1 ≤5 Therefore, shade the half-plane with the point. Jeff Bivin -- LZHS

  9. y = 2x + 1 y ≤2x + 1 What if we picked a point on the other side of the line? Don't Shade Let’s try (-2, 3) Does the point satisfy the inequality? Shade 3 ≤2(-2) + 1 3 ≤ -4 + 1 3 ≤-3 FALSE Therefore, shade the otherhalf-plane opposite the point. Jeff Bivin -- LZHS

  10. y = -3x + 2 y ≥-3x + 2 Run 1 y-intercept Rise b = 2 -3 slope m = -3 Jeff Bivin -- LZHS

  11. y = -3x + 2 y ≥-3x + 2 Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Shade Does the point satisfy the inequality? Don't Shade 0 ≥-3(0) + 2 0 ≥0 + 2 FALSE 0 ≥2 Therefore, shade the other half-plane opposite the point. Jeff Bivin -- LZHS

  12. Run 3 y-intercept b = -1 Rise 2 slope Jeff Bivin -- LZHS

  13. Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Shade Does the point satisfy the inequality? TRUE Therefore, shade the half-plane with the point. Jeff Bivin -- LZHS

  14. When dealing with just x and y. • If the sign > or  the shading either goes up or to the right • If the sign is < or  the shading either goes down or to the left

  15. 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.

  16. Here is a graph of y  3.

  17. One and Done • Monday What kind of boundary line should be drawn for the graph of the line y< -4x + 3?

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