Graphing Linear Inequalities
in Two Variables
LESSON ESSENTIAL QUESTION:
How do you graph an
inequality?
WARMUP
Complete Day 4 Warmup Problems
Shade, Shade, Shade, Shade It
• http://teachertube.com/viewVideo.php?video
_id=121267
Put the equations into y=mx+b form to graph!
Graphing Review
Graph each line.
a) y = x + 2
b)
x – 2y = 6
Graphing a Linear Inequality
Graphing a linear inequality is very
similar to graphing a linear
equation.
Graphing Inequalities
Where do you think the points that are y > x + 2 are located?
Where do you think the points that are y < x + 2 are located?
Graphing Inequalities
The line is the boundary of the two regions. The blue region is the
“greater than” (>) area and the yellow region is the “less than” (<)
area.
YOU WERE
RIGHT!!
Graphing Inequalities
When the line that represents y = x + 2 is solid, not dashed, it means
that the points on the line are included in the inequality. So we would
state that the blue are can be represented by
y  x + 2. And, the yellow could
be represented by y  x + 2.
Graphing Inequalities
When the line that represents y = x + 2 is dashed, it means that the
points on the line are not included in the inequality. So we would
state that the blue are can be represented by y > x + 2.
And, the yellow could be
represented by y < x + 2.
Tell Your Neighbor
• What does it mean to
be a point in the
solution of an
inequality?
– A point in the shaded
area of the solution set
that fits the inequality
• Name 1 point in the
solution set
• Name 1 point NOT in
the solution set
Steps to Graphing Linear Inequalities
1. Change the inequality into slope-intercept form,
y = mx + b. Graph the equation.
2. If > or < then the line should be dashed.
If > or < then the line should be solid.
3. If y > mx+b or y > mx+b, shade above the line.
If y < mx+b or y < mx+b, shade below the line.
4. To check that the shading is correct, pick a point in
the area and plug it into the inequality
–
–
If TRUE, you shaded correct
If FALSE, you shaded incorrectly
GRAPHING INEQUALITIES
INEQUALITY
SYMBOL
TYPE OF LINE
(dashed or solid)
WHERE TO SHADE
<
>
≤
≥
dashed
below
dashed
above
solid
below
solid
above
(above or below line)
GRAPHING INEQUALITIES
SOLID LINE
DASHED
LINE
SHADE UP
SHADE BELOW
≥
≤
>
<
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.
y
Boundary Line
-
y = 3x + 2
-
m= 3
3

1
b=2
x
Test a point not on the line
test (0,0)
0
-3(0) + 2
Not true!
Graph y  -3x + 2 on the coordinate plane.
y
Instead of testing a point
If in y = mx + b form...
Shade
up
Solid
line
Dashed
line

>
Shade
down

<
x
Surfing with Inequalities
• Will the inequality “surf” splash
over our surfer?
• Step 1: Graph line
• Step 2: Dashed or solid line?
• Step 3: Shade above or below
line?
• Step 4: Verify a point
y ≥ 2x
Using What We Know
Sketch a graph of x + y < 3
Step 1: Put into
slope intercept form
y <-x + 3
Step 2: Graph the
line y = -x + 3
STEP 1
Example:
2
y  x4
3
1. 2x  3y  12
6
STEP 3
4
STEP 2
2
5
Graph on the coordinate plane.
3x - 4y > 12
-3x
-3x
-4y > -3x + 12
-4
-4
3
y < x-3
4
Boundary Line
3
m=
4
b = -3
y
Remember that when you
multiply or divide by a
negative number..FLIP THE
INEQUALITY SIGN!!
x
STEP 1
Example:
2. x  3 y > 6
6
STEP 2
4
STEP 3
2
5
1
y< x2
3
Graphing a Linear Inequality
Sketch a graph of y  3
Graphing an Inequality in Two Variables
Graph x < 2
Step 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.
HOMEWORK
• Complete the kuta worksheet
Surfing with Inequalities
• Will the inequality “surf”
splash over our surfer?
• Decide if the shading of
inequality (the surf) will
splash over the surfer.
2y > 10-x
7.5 Practice
•
•
•
•
Graph each inequality.
Determine if the given point is a solution.
Do # 1-3
Check solution with your neighbor
Example:
3. x  1
STEP 1
6
STEP 2
4
STEP 3
2
-5
5
-2
CLASSWORK
• Complete the surfing
with inequalities wsht
• Turn in for a graded
classwork assignment
• Be accurate with your
graphing
• Be careful when
dividing by a negative #
Absent Student Letter
• Write a letter to an absent student explaining
what an inequality is and how to graph a
system of inequalities?
The solution to a system of Equations is the POINT of INTERSECTION
Graphing Review
Use a graph to solve each system of equations.
a) y = x + 1 and y = -x + 3
b)
2x – y = 6 and y = x - 2