How do you model a problem in which you
have two or more variables that must total
less than a specific amount?
For example, how can you find how many of
each type of stamp you need on a package
that requires an exact amount of postage?
In this lesson you will learn how to
represent solutions and constraints
to linear inequalities by graphing.
Let’s Review
You can graph an inequality in two variables.
5x + 6y ≤ 30
A Common Mistake
Not accounting for a constraint
Can’t I just keep
adding stamps until
I have enough
money?
If you only have
certain kinds of
stamps, you might
pay too much!
Core Lesson
You need $1.00 worth of postage to mail a
package.
Entire book of $0.03 stamps but only four
$0.32 stamps
How many of each type can you use?
Core Lesson
(amount of
money using
$0.03 stamps)
(amount of money
+
≥ $1.00
using $0.32
stamps)
$0.03(x) + $0.32(y) ≥ $1.00
Core Lesson
$0.03(x) + $0.32(y) ≥ $1.00
Constraints:
1. Positive
numbers only
2. Whole numbers
You will need at least 12 $0.03 stamps and 2
$0.32 stamps.
In this lesson you have learned
how to represent solutions and
constraints to linear inequalities by
graphing.
Guided Practice
Your school needs at least 35 students to
help volunteer at a shelter downtown. Seven
students can ride to the shelter in each van,
and five students can ride in each car. Draw
a graph showing all of the combinations of
vans and cars possible for the problem.
Guided Practice
Extension Activities
Choose two types of fruit, such as strawberries
and watermelon. Write an equation for and graph
a linear inequality to show how much of each fruit
you could buy without spending more than $10
total.
Extension Activities
Draw a polygon on a coordinate plane. Write a
series of linear inequalities that, graphed and
shaded correctly, would result in the given
polygon.
Quick Quiz
An air cargo plane can transport as many as
15 regular shipping containers. One supersized container takes up the space of 3
regular containers. Write and graph a linear
inequality to show this situation, and find
two solutions to this problem.
Quick Quiz
Your school needs at least 35 students to
help volunteer at a shelter downtown.
Seven students can ride to the shelter in
each van, and five students can ride in each
car. Find the minimum number of cars
needed if three vans are available.