Download 5-7a Graph a Linear Inequality in the

Linear Inequalities
Honors Math – Grade 8
Graphing Linear Inequalities in
Two Variables

The solution set for an inequality in two
variables contains many ordered pairs
when the domain and range are the set of
real numbers.
Key Concept
Any line in the
plane divides the
plane into two
regions called
half planes. The
line is called the
boundary of
each of the two
half-planes.
Graphing the boundary line is
the first step in graphing an
inequalities solution.
Half Plane
Boundary
Line
Half Plane
y4
1. Determine the equation of
the boundary line by replacing
the inequality sign with an
equals sign.
y4
y4
2. Graph the equation of the
boundary line.
Dashed Line - used to graph >
or < inequalities because the
boundary is not part of the
solution set.
x
y
0
4
1
4
2
4
3. Choose a point
in each half plane.
Test each point in
the inequality.
4. Shade the entire
half-plane whose point
gave a true statement.
1
y  x3
2
1. Determine the equation of the
boundary line by replacing the
inequality sign with an equals
sign.
y
1
x3
2
2. Graph the
equation of the
boundary line.
y
1
x3
2
m = 1/2
y-int = 3
Dotted Line because inequality is >.
3. Choose a point
in each half plane.
Test each point in
the inequality.
Use the origin
as a standard
test point.
Since (0, 0) gives a
false statement, shade
the other half-plane.
y  2 x  4
1. Determine the equation of the
boundary line by replacing the
inequality sign with an equals
sign.
y  2 x  4
y  2 x  4
2. Graph the equation of the
boundary line. Solve for y.
Solid Line - used to graph > or <
inequalities because the boundary is
part of the solution set.
3. Choose a point
in each half plane.
Test each point in
the inequality.
Use the origin
as a standard
test point.
Since (0, 0) gives a
false statement, shade
the other half-plane.
x  1
1. Determine the equation of
the boundary line by replacing
the inequality sign with an
equals sign.
x  1
x  1
2. Graph the equation of the
boundary line.
Solid Line - used to graph > or
< inequalities because the
boundary is part of the solution
set.
x
y
-1
4
-1
4
-1
4
3. Choose a point
in each half plane.
Test each point in
the inequality.
4. Shade the entire
half-plane whose point
gave a true statement.
 4x  2 y  6
1. Determine the equation of the
boundary line by replacing the
inequality sign with an equals
sign.
 4x  2 y  6
 4x  2 y  6
2. Graph the equation of the
boundary line. Standard Form.
Dotted Line because inequality is >.
3. Choose a point
in each half plane.
Test each point in
the inequality.
Use the origin
as a standard
test point.
Since (0, 0) gives a
false statement, shade
the other half-plane.
One solution is Lee
could write 2 articles
and edit 4.
Define the
variables
Let x = the # of articles
Lee can write and y =
the # of articles Lee can
edit.
The # of articles she can write + ½ times the
number she can edit is up to 8 hours.
1
x y 8
2
1
x y 8
2
1. Determine the equation of
the boundary line.
2. Graph the equation of the
boundary line. Solve for y.
Solid Line because inequality is <.
Lee Cooper writes and edits short articles for a
local newspaper. It takes her about an hour to
write an article and about a half-hour to edit an
article. If Lee works up to 8 hours a day, how
many articles can she write and edit in one
day?
Write an open sentence representing this
situation.
3. Choose a
point in each
half plane.
Use the origin
as a standard
test point.
Since (0, 0) gives a true statement, shade
the half-plane but not negative integers.
Tickets for the school play cost $5 for students
and $7 for adults. The school wants to earn at
least $6300 on each performance.
Define the
variables
Let x = the # of student
tickets and y = the # of
adult tickets.
5 times the # of student tickets + 7 times the
number of adult tickets is at most $6300
5 x  7 y  6300
5 x  7 y  6300
1. Determine the equation of
the boundary line.
2. Graph the equation of the
boundary line. Solve for y.
Solid Line because inequality is <.
One solution is the school could sell 600 student tickets
and 650 adult tickets.
Write an open sentence representing this
situation.
3. Choose a
point in each
half plane.
Use the origin
as a standard
test point.
Since (0, 0) gives a false statement,
shade the other half-plane.