2.8 Graphing Linear Inequalities in Two Variables

Graphing Vertical and Horizontal lines We graph the inequalities the same as

equations, but with a couple of differences….

Put in form of y = mx + b

Find the slope and the y-intercept

Dashed or Solid If an inequality has a < or >, then draw a

dashed line. If an inequality has a , then draw a

solid line. or

Shading < and is shaded below the line

> and is shaded above the line.

If you are not sure which side of the line to shade, plug in any point as a test. You need to use a point that is NOT on the line.

(0,0) are (1,1) are usually good test points to use, as long as the point you choose is not on the line.

Example: y < x + 3

Line is dashed because it is <,

The line is shaded below and to the right of the line.

Any and All of the points in the shaded area are part of the solution.

slope is 1, y intercept is at (0,3)

Example: y ≥ 2x -1

Line is solid because it is ≥,

Plug in (0,0) as a test point:0 ≥ 0 – 1 ---TRUE, so (0,0) is in the shaded area.Shaded above and to the left of the line.

slope is 2, y intercept is at (0,-1)

y > -x + 2

Plug in (0,0)

0 > 0 + 2

0 > 2NOT TRUE

Lines with Slope

1. Decide whether your line is solid or dashed.

2. Rewrite the inequality as an equation in y = mx + b form.

3. Graph using the y-intercept and slope.

4. Plug a test point {usually (0, 0)} to determine on which side of the line you should shade.

Classwork Practice

Page 118, #8-16

Graphing Absolute Value Inequalities

y < |x-2| + 3

This is in the formy = a |x-h| + k

So the vertex is(2,3) and the right side of the “V” has a slope of 1.

Since y < |x-2| + 3Shade below the graph

Graphing Absolute Value Inequalities

y ≥ ½ |x+2|

Graphing Absolute Value Inequalities

y > -2 |x-1| - 4

Classwork

Text page 118, #8-16 All, and #19-29 odd