Download 6.5 Graphing Linear Inequalities in Two Variables

6.5 Linear Inequalities
Standard: SWBAT
sketch the region
defined by linear
inequality
Chapter 6
Algebra 1
Ms. Mayer
Overview
-
-
Graphing Linear Inequalities
Solid or Dotted
Which Side to Shade
Writing Inequalities from a graph
Graphing Linear Inequalities in Two
Variables
How would you graph the equation x + y = 3?
x+y=3
-x
-x
y = -x + 3
m = -1
b=3
What
happens if the
“=“ changes
to “≤” or “≥”?
We get
shading!!!
=≤
Graph x + y ≤ 3
Pick a point not on
the line to find out
which side to shade.
If it’s true, shade
same side. If not,
shade the opposite
side!
=≥
Graph x + y ≥ 3
What point do you
want to pick?
Solid or dashed?
The lines can be graphed as a solid line or a
dashed (dotted) line. When do you think it’s
solid, and when is it dashed? Think about
graphing points on a number line; when is it
open and when is it closed?
< or > is …
≤ or ≥ is …
Graphing Linear Inequalities
Steps:
1. Graph the equation (solve for y)
2. Draw a Dotted or Solid line
3. Pick a point not on a line (any point)
4. Shade the correct side
-
True – shade the same side
False – shade the opposite side
Graph These…
1. y < -2
Graph These…
2. -1 ≤ x + y
Graph These…
3. x > 4
Graph These…
4. x – 3y ≤ 12
Writing an Inequality
Write an inequality for each graph.
5.
6.
y  x2
1
y  x3
3
Writing an Inequality
Write an inequality for each graph.
7.
8.
x3
y  2
Application
9. Suppose your budget for a party allows you to
spend no more than $12 on peanuts and cashews.
Peanuts cost $2/lb and cashews cost $4/lb. Find
three possible combinations of peanuts and
cashews you can buy.
x = number of pounds of peanuts
y = number of pounds of cashews
2x + 4y ≤ 12
Wrap Up
Graphing Inequalities
 Solid line/Dotted line
 Shading
HW: P. 305 #1-23 odd; P. 308 #1-4 all
Write DLUQ for notes.