This document contains notes from mathematics lessons on representing proportional relationships with equations. It includes examples of setting up proportional relationships between variables like gallons of gas used and miles driven. Students are given practice problems to determine constants of proportionality from tables and graphs, then using the proportional relationships to solve problems algebraically. The document also provides solutions to these practice problems.

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Representing Proportional Relationships
with Equations
09/11/15Module 7.1 Lessons 8 and 9
Homework:
1.) Lesson 8 Problem
Set #3-5
2.) Lesson 9 Problem
Set #1, 4
Do Now
Exit Ticket from Lesson 7
Mid Module Assessment
Friday 9/18/15

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Exit Ticket

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TableProblem
Graph Proportional or Not?
Explain.
Years Total Money
Years
Money
title
1 yr, $312
3 yr, $340
6 yr, $380
9 yr, $430
12 yr, $480
Lesson 6 Problem Set #1 S.22

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S.22

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S.27

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Problem Set Solutions (continued) S.27

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Problem Set Solutions (continued)
S.27

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S.28

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S.29

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a. Find the constant of proportionality and explain what it
represents in this situation.
Gallons Miles Driven
y
x
8 224
10 280
4 112

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b. Write the equation that will relate the miles driven to the number
of gallons of gas.
Steps to figure out the equation.
1. Which unit is the dependent variable?
2. Which unit is the independent variable?
3. Find the k.
Constant of Proportionality = k =
4. Plug in the value of k to y = kx.
­The constant
x is known as the independent
variable and
y as the dependent variable,.

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c. Knowing that there is a half gallon left in the gas tank when the light
comes on, will she make it to the nearest gas station? Explain why or
why not.
Using Arithmetic Using Algebra
d. Using the equation found in part b, determine how far your mother
can travel on 18 gallons of gas. Solve the problem in two ways.

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e. Using the equation found in part b, determine how many gallons of gas
would be needed to travel 750 miles.

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a. Write several ordered pairs from the graph
and explain what each coordinate pair means
in the context of this graph.
S.30

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b. Write several equations that would relate the number of
portraits drawn to the time spent drawing the portraits.
c. Determine the constant of proportionality and explain what it
means in this situation.

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Problem Set S.31

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Problem Set
S.32

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Problem Set S.35
a. Which variable is the dependent variable and why?
b. Is miles driven proportionally related to gallons of gas consumed? If
so what is the equation that relates miles driven to gallons?
c. In any ratio relating gallons and miles driven, will one of the values
always be larger, if so, which one?

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Problem Set S.35
d. If the number of gallons is known, can you find the miles driven? Explain
how this value would be calculated.
e. If the number of miles driven is known, can you find the number of
gallons consumed?
f. How many miles could be driven with 18 gallons of gas?

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Problem Set S.35
g. How many gallons are used when the car has been driven 18 miles?
h. How many miles have been driven when ½ of a gallon is used?
i. How many gallons have been used when the car has been driven ½ mile?

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Problem Set S.36

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Define the variables B and H:
Determine the number of birdhouses that can be built in one hour.
What is the constant of proportionality?
S.33

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dependent variable = k(independent variable)
We want to know how long it will take to build any number of birdhouses.
What is the dependent variable?
Constant of Proportionality =
k =
Write the equation using this format.
S.33

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S.33

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Which makes more sense:
**First, we need to find the constant of proportionality (unit rate)
for each produce stand.
(cost)
"# of ears of corn per dollar" or "dollars per ear of corn"
S.34

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Which makes more sense:
**First, we need to find the constant of proportionality (unit rate)
for each produce stand.
"# of ears of corn per dollar" or "dollars per ear of corn"
(cost)

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How do you determine which value is x (independent) and which value is
y (dependent)?

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