graphing linear inequalities in two variables graph a linear inequality in two variables model a...
TRANSCRIPT
Graphing Linear Inequalities in Two
Variables•graph a linear inequality
in two variables
•model a real life situation with a linear inequality.
Recall…Graph n < 3 on a number line.
-3 -2 -1 0 1 2 3 4
Graphing an Inequality in Two Variables
Graph x < 2Step 1: Start by graphing the line x = 2
Now what points would give you less
than 2?
Since it has to be x < 2 we shade everything to
the left of the line.
Graph x -2 on the coordinate plane.
x
y
Graph y > 3 on the coordinate plane.
x
y
Graphing a Linear Inequality
Sketch a graph of y 3
Some Helpful Hints
•If the sign is > or < the line is dashed
•If the sign is or the line will be solid
When dealing with just x and y.
•If the sign > or the shading either goes up or to the right
•If the sign is < or the shading either goes down or to the left
Using What We KnowSketch a graph of x + y < 3
Step 1: Put into slope intercept form
y <-x + 3
Step 2: Graph the line y = -x + 3
When dealing with slanted lines
•If it is > or then you shade above
•If it is < or then you shade below the line
Graph y -3x + 2 on the coordinate plane.
x
y
Instead of testing a point
If in y = mx + b form...
Shade up
Shadedown
Solid line
Dashed line
> <
Graph on the coordinate plane.
3x - 4y > 12-3x -3x-4y > -3x + 12-4 -4
y < x - 33
4
m =
b = -3
3
4
Boundary Linex
y
Graph y -3x + 2 on the coordinate plane.
x
y
Boundary Line
y = -3x + 2
m = -3
b = 2
3
1
Test a point not on the linetest (0,0)
0 -3(0) + 2Not true!
ProblemIf you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have.
Let n = # of nickelsLet d = # of dimes
0.05 n + 0.10 d < 5.00
or
5 n + 10 d < 500
5n + 10d < 500n d
0 50
100 0
0 10 20 30 40 50 60 70 80 90 100n
d
60
50
40
30
20
10
0
Graphing Absolute Value Inequalities
xy 2
Graphing Absolute Value Inequalities
21 xy