This document contains notes from a math lesson on proportional relationships and equations. It includes examples of proportional word problems about building birdhouses, produce stands, and gas mileage. It provides the homework, which is to complete problem sets and an exit ticket from the previous lesson. The notes define proportional relationships and show how to write equations in the form of y=kx to model these relationships using constants of proportionality.

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Representing Proportional Relationships
with Equations
09/24/15
Module 1, Lesson 9
Homework:
Lesson 9 Problem
Set #1, 4
Do Now
Exit Ticket from Lesson 8
(IT IS TWO PAGES)
Quiz 1 Tuesday 9/29

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Lesson 8 Exit Ticket

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S.31

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S.31­32

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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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Solving Equations Mini-Lesson
a.) 10 = x
4
5
b.) y = (15)
4
5

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Solving Equations Mini-Lesson
a.) 17 = x
3
2
b.) y = (11)
3
2

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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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Is it possible to work part of an hour?
Will a customer want to buy part of a birdhouse?

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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"

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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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What will we use for the independent variable?
Which would be the dependent varialbe and why?
Write the equation for each produce stand:
Al's Produce Stand Barbara's Produce Stand

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Questions to Consider
What type of relationship can be modeled using an equation in the form y =
kx, and what do you need to know to write an equation in this form?
Give an example of a real­world relationship that can be modeled using this
type of equation and explain why.
How do you determine which value is x (independent) and which value is
y (dependent)?
Give an example of a real­world relationship that cannot be modeled using
this type of equation and explain why.

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