5.6 – Graphing Inequalities in
Two Variables
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(x, y)
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(x, y)
3x + 2y < 12
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(x, y)
3x + 2y < 12
True or False
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(x, y)
(1,6)
3x + 2y < 12
True or False
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(x, y)
3x + 2y < 12
(1,6) 3(1) + 2(6) < 12
True or False
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(x, y)
3x + 2y < 12
(1,6) 3(1) + 2(6) < 12
True or False
False
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(x, y)
(1,6)
(3,0)
(2,2)
(4,3)
3x + 2y < 12
3(1) + 2(6) < 12
3(3) + 2(0) < 12
3(2) + 2(2) < 12
3(4) + 2(3) < 12
True or False
False
True
True
False
Ex. 1 From the set {(1,6),(3,0),(2,2),(4,3)},
which ordered pairs are part of the solution
set for 3x + 2y < 12?
(3,0) & (2,2)
(x, y)
(1,6)
(3,0)
(2,2)
(4,3)
3x + 2y < 12
3(1) + 2(6) < 12
3(3) + 2(0) < 12
3(2) + 2(2) < 12
3(4) + 2(3) < 12
True or False
False
True
True
False
Ex. 2 Graph y > 3
Ex. 2 Graph y > 3
Ex. 2 Graph y > 3
1) Go to where y = 3
Ex. 2 Graph y > 3
1) Go to where y = 3
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
2) Vertical
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
2) Vertical, Solid
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
2) Vertical, Solid
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
2) Vertical, Solid
3) Shade inequality
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
2) Vertical, Solid
3) Shade inequality
Ex. 2 Graph y > 3
1) Go to where y = 3
2) Horizontal, Dashed
3) Shade inequality
Ex. 3 Graph x < -1
1) Go to where x = -1
2) Vertical, Solid
3) Shade inequality
Ex. 4 Graph y – 2x < -4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
LINE: Solid b/c includes
“equal to”
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
LINE: Solid b/c includes
“equal to”
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
LINE: Solid b/c includes
“equal to”
SHADE: Since < shade
below the line.
Ex. 4 Graph y – 2x < -4
y – 2x < -4
+2x +2x
y < 2x – 4
GRAPH: y = 2x – 4
m = 2, b = -4
LINE: Solid b/c includes
“equal to”
SHADE: Since < shade
below the line.
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Let y = # of child tickets.
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Let y = # of child tickets.
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Let y = # of child tickets.
Total number of people cannot exceed
250.
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Let y = # of child tickets.
Total number of people cannot exceed
250. So, x + y
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Let y = # of child tickets.
Total number of people cannot exceed
250. So, x + y < 250
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Let y = # of child tickets.
Total number of people cannot exceed
250. So, x + y < 250
OR
Ex. 5 Suppose a theatre can seat a
maximum of 250 people. Write an
inequality to represent the number of
adult and childrens tickets that can be
sold.
Let x = # of adult tickets.
Let y = # of child tickets.
Total number of people cannot exceed
250. So, x + y < 250