1. 2.8 Graphing Linear Inequalities in Two Variables

2. 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

3. Dashed or Solid
If an inequality has a < or >, then draw a dashed line.
If an inequality has a , then draw a solid line.

4. Shading < and is shaded below the line
> and is shaded above the line.

5. 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.

6. Example: y < x + 3 slope is 1, y intercept is at (0,3)
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.

7. Example: y ≥ 2x -1 slope is 2, y intercept is at (0,-1)
Line is solid because it is ≥,
Plug in (0,0) as a test point:
0 ≥ 0 – TRUE, so (0,0) is in the shaded area.
Shaded above and to the left of the line.

8. y > -x + 2
Plug in (0,0)
0 > 0 + 2
0 > 2
NOT TRUE

9. Lines with Slope Decide whether your line is solid or dashed.
Rewrite the inequality as an equation in y = mx + b form.
Graph using the y-intercept and slope.
Plug a test point {usually (0, 0)} to determine on which side of the line you should shade.

10. Classwork Practice
Page 118, #8-16

11. Graphing Absolute Value Inequalities
y < |x-2| + 3
This is in the form
y = 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| + 3
Shade below the graph

12. Graphing Absolute Value Inequalities
y ≥ ½ |x+2|

13. Graphing Absolute Value Inequalities
y > -2 |x-1| - 4

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