This document appears to be notes from a math lesson on representing proportional relationships with equations. It includes examples of finding the constant of proportionality from data sets and using it to write equations relating variables. Students are asked to determine constants of proportionality, write proportional equations, and solve problems algebraically and arithmetically using the equations. The document emphasizes that the constant of proportionality is the unit rate and can be used to write an equation relating proportional variables.

1. Module 1 Lesson 8.notebook
1
September 24, 2013
Representing Proportional Relationships
with Equations
Homework: Lesson #8 Problem Set
Do Now: Discuss Lesson #7 Problem Set with Partner
09/24/13
Module 1, Lesson 8

2. Module 1 Lesson 8.notebook
2
September 24, 2013
Problem Set Solutions (continued)

3. Module 1 Lesson 8.notebook
3
September 24, 2013
Problem Set Solutions (continued)

4. Module 1 Lesson 8.notebook
4
September 24, 2013
Yesterday's Exit Ticket

5. Module 1 Lesson 8.notebook
5
September 24, 2013

6. Module 1 Lesson 8.notebook
6
September 24, 2013

7. Module 1 Lesson 8.notebook
7
September 24, 2013
a. Find the constant of proportionality and explain what it
represents in this situation.
Gallons Miles Driven
8 224
10 280
4 112

8. Module 1 Lesson 8.notebook
8
September 24, 2013
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 usually known as the
independent variable and
y as the dependent variable,.

9. Module 1 Lesson 8.notebook
9
September 24, 2013
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.

10. Module 1 Lesson 8.notebook
10
September 24, 2013
e. Using the equation found in part b, determine how many gallons of gas
would be needed to travel 750 miles.

11. Module 1 Lesson 8.notebook
11
September 24, 2013
a. Write several ordered pairs from the graph
and explain what each coordinate pair means
in the context of this graph.

12. Module 1 Lesson 8.notebook
12
September 24, 2013
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.

13. Module 1 Lesson 8.notebook
13
September 24, 2013

14. Module 1 Lesson 8.notebook
14
September 24, 2013
Closing Question
How can unit rate be used to write an equation
relating two variables that are proportional?
The unit rate is the constant of proportionality, k. After
computing the value for k, it may be substituted in place of k in
the equation y = kx. The constant of proportionality can be
multiplied by the independent variable to find the dependent
variable, and the dependent variable can be divided by the
constant of proportionality to find the dependent variables.

15. Module 1 Lesson 8.notebook
15
September 24, 2013

16. Module 1 Lesson 8.notebook
16
September 24, 2013