7.RP.2 Recognize and represent proportional relationships between quantities.
b. Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional
relationships.
c. Represent proportional relationships by equations. For example, if total
cost, t, is proportional to the number, n, of items purchased at a constant
price, p, the relationship between the total cost and the number of items
can be expressed at t = pn.
d. Explain what a point (x, y) on the graph of a proportional relationship
means in terms of the situation, with special attention to the points (0,0)
and (1, r), where r is the unit rate.
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem,
and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x +
q) = r where p, q, and r are specific rational numbers. Solve equations of
these forms fluently. Compare an algebraic solution to an arithmetic
solution, identifying the sequence of the operations used in each approach.
For example, the perimeter of a rectangle is 54cm. Its length is 6cm. What
is its width?
7.1.8
7.1.9
7.1.10

Students use the constant of proportionality to represent proportional
relationships by equations in real-world contexts as they relate the equations to
a corresponding ratio table and/or graphical representation.
WKSP
HW
Media
Student
Learning Goal
CC
Lesson
Standard
Pre Requisite
Proportionality in Equations
#49
Spiral Review #13
Proportionality in Equations
Proportional relationships have a constant ratio, or ____________.
The constant ratio of
𝑦
𝑥
can also be called the ________________________________.
What is the formula for the constant of proportionality?
Andrea’s Portraits
Andrea is a street artist in New Orleans. She draws caricatures of tourists.
People have their portrait drawn and then come back later to pick it up
from her. The graph below shows the relationship between the number of portraits she
draws and the amount of time in hours she needs to draw the portraits.
Write several ordered pairs from the graph and explain what each ordered pair means
in the context of this graph.
Determine the constant of proportionality and explain what it means in this situation.
How can unit rate be used to write an equation relating two variables that are
proportional?
Write an equation representing this situation using the constant of proportionality.
Proportionality in Equations
Al’s Produce Stand
Al’s Produce Stand sells 6 ears of corn for $1.50. Barbara’s Produce Stand sells 13 ears
of corn for $3.12. Write two equations, one for each produce stand, that models the
relationship between the number of ears of corn sold and the cost. Then use each
equation to help complete the tables below.
Which makes more sense: number of ears of corn per dollar or cost per ear of corn?
What is the constant of proportionality for Al’s Produce Stand?
What is the constant of proportionality for Barbara’s Produce Stand?
How do we write an equation for a proportional relationship?
Write an equation for Al’s Produce Stand:
Write an equation for Barbara’s Produce Stand:
Exercise:
1. There are 3 cans that store 9 tennis balls. Consider the number of tennis balls per
can.
a. Find the constant of proportionality.
b. Write an equation to represent the relationship.
2. It cost $15 to send 3 packages through a certain shipping company. Consider the
number of packages per dollar.
a. Find the constant of proportionality for this situation.
b. Write an equation to represent the relationship.
Proportionality in Equations
Name: __________________________________
Pre-Algebra
Date: ______
Exit Ticket
In 25 minutes, Li can run 10 laps around the track. Determine the number of laps she
can run per minute.
Find the constant of proportionality in this situation.
Write an equation to represent the relationship.
Name: __________________________________
Pre-Algebra
Date: ______
Exit Ticket
In 25 minutes, Li can run 10 laps around the track. Determine the number of laps she
can run per minute.
Find the constant of proportionality in this situation.
Write an equation to represent the relationship.
Proportionality in Equations
Name: _______________________________________
Pre-Algebra
Date: _____
HW #49
Lesson Summary
The constant of proportionality expresses the multiplicative relationship between each x-value and its
corresponding y-value.
1.
John and Amber work at an ice cream shop. The hours worked and wages earned
are given for each person.
Determine if John’s wages are proportional to time. If they are, determine the unit
𝑦
rate of 𝑥 . If not, explain why they are not.
Determine if Amber’s wages are proportional to time. If they are, determine the
𝑦
unit rate of 𝑥 . If not, explain why they are not.
Write an equation for both John and Amber that models the relationship between
their wage and the time they worked. Identify the constant of proportionality for
each. Explain what it means in the context of the situation.
How much would each worker make after working 10 hours? Who will earn more
money?
How long will it take each worker to earn $50?
Proportionality in Equations
Review:
2. Simplify 2 + 1 (1 𝑓 − 1 1)
3
3 4
3