Transcript Graphing Linear Inequalities in Two Variables

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 yintercept
Dashed or Solid


If an inequality has a < or >, then draw a
dashed line.
If an inequality has a  or , then draw a
solid line.
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
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.
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 – 1 ---TRUE,
so (0,0) is in the
shaded area.
Shaded above and
to the left of the line.
y > -x + 2
Plug in (0,0)
0>0+2
0>2
NOT TRUE
Lines with Slope
1.
2.
3.
4.
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.
Classwork Practice

Page 118, #8-16
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
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