Title: 2.8 Graphing Linear Inequalities in Two Variables
12.8 Graphing Linear Inequalities in Two Variables
2Graphing 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
3Dashed or Solid
- If an inequality has a lt or gt, then draw a dashed
line. - If an inequality has a , then draw
a solid line.
4Shading
- lt and is shaded below the line
- gt 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.
6Example y lt x 3
slope is 1, y intercept is at (0,3)
Line is dashed because it is lt, 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.
7Example 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 1 ---TRUE, so (0,0) is
in the shaded area. Shaded above and to the left
of the line.
8y gt -x 2
Plug in (0,0) 0 gt 0 2 0 gt 2 NOT TRUE
9Lines 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.
10Classwork Practice
11Graphing Absolute Value Inequalities
y lt 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 lt x-2 3 Shade below the graph
12Graphing Absolute Value Inequalities
y ½ x2
13Graphing Absolute Value Inequalities
y gt -2 x-1 - 4
14ClassworkText page 118, 8-16 All, and
19-29 odd