Warm Up: Wed, 01/21/15 Solve for x: 2x < -10 -3x > 9

Graphing Linear Inequalities 01/21/15

Inequality Symbol Type of Line > or < Dotted Line Solid Line How to Determine the Type of Line to Draw Inequality Symbol Type of Line > or < Dotted Line Solid Line

Choose the type of line for the inequality given. 1. y > 3x - 2 a. Solid b. Dotted 2. y > ¼x - 5

Choose the inequality symbol for the line shown.

Choose the inequality symbol for the line shown.

If the inequality is: Shade y > mx + b or Above the line y < mx + b Below the line

Graph y > x - 2. 1. Graph the line y = x - 2. x 2. Since y >, shade above the line. y

Graph y < x - 2. 1. Graph the line y = x - 2. x 2. Since y <, shade below the line. y

Do you do anything different when the line is dotted rather than solid? Lesson Start

Not Really Lesson Start

Finally…Check your shading! The shading indicates that that coordinate is a solution for your inequality. If it is a solution, you can plug in the coordinates to the inequality and it will be true.

What to do: Choose any point in the area you are shading Plug in for x and y Simplify your expression Does it make the inequality true? Then it IS a solution. If it is false, it is NOT a solution. If it is a solution, shade that side of the line. If it’s NOT, shade the other side.

Let’s check! y < x - 2. 1. Graph the line y = x - 2. x 2. Since y <, shade below the line. y

Now do #1 on your blue worksheet. Stop! Now do #1 on your blue worksheet.

Choose the correct inequality for the graph shown. y < 1/3 x + 2 y < 1/3 x + 2 x y > 1/3 x + 2 y > 1/3 x + 2 y

FRIDAY 01/23/15

Happy Aloha Friday! (01/23) Please take out your Math Review notebook. We will have a short quiz. Please raise your hand and I will correct.

Math Review Quiz Solve for x: 2x – 2 < 16 (2 pts) Graph #1 on a number line. (2 pts)

Essential Question What does it mean if a linear function has no x or y intercept?

What do you notice about this graph? x y

  Therefore, your equation will be x>1, because it intersects the x-axis at (1,0), and is shaded right. x y

Can you guess the inequality for this line? x y

The inequality for this line is going to be y < -1 b/c there is no x-intercept (and no slope), and is shaded down. x y

If the inequality is: Shade To the x > # or Right of the line x < # Left of the line

Practice Please do #21 and #26 on your Wednesday worksheet [blue].

Graph x > -2 1. Draw a dotted vertical line at x = -2. x 2. Shade to the right of the line. y

Graph x < -2. 1. Graph the line X = -2. x 2. Shade to the left of the line. y

Graph x > 3. Choose type of line. Solid Dotted x y

Graph x > 3. Choose type of line. Solid Choose where to shade. Left Right y

Graph x > 3. Choose type of line. Solid Choose where to shade. Right y

Solve -3x - 2y < 12. +3x +3x -2y < 3x + 12 -2 -2 -2 y < -3/2 x - 6 >

Choose the correct inequality. 1. 2x + 5y > -10

Example 1 Which ordered pair is a solution of 5x - 2y ≤ 6? (0, -3) (5, 5) (1, -2) (3, 3) ANSWER: A. (0, -3)

Example 2 Graph the inequality x ≤ 4 in a coordinate plane. Decide whether to use a solid or dashed line. Use (0, 0) as a test point. Shade where the solutions will be. y x 5 -5

Example 3 Graph 3x - 4y > 12 in a coordinate plane. Sketch the boundary line of the graph. Solve for “y” first: y < ¾x - 3 Solid or dashed line? Use (0, 0) as a test point. Shade where the solutions are. y x 5 -5

Example 4: Graph y < 2/5x in a coordinate plane. What is the slope and y-intercept? m = 2/5 b = (0,0) Solid or dashed line? Use a test point OTHER than the origin. Shade where the solutions are. y x 5 -5

Graph: y ≥ -3/2x + 1 Step 1: graph the boundary (the line is solid ≥) Step 2: test a point NOT On the line (0,0) is always The easiest if it’s Not on the line!! 3(0) + 2(0) ≥ 2 0 ≥ 2 Not a solution So shade the other side of the line!!

Graph: y < 6

Graph: 4x – 2y < 7