This document provides instruction on identifying proportional relationships and calculating slope. It includes examples of finding the constant rate of change from tables and graphs, as well as calculating slope from points on a line. The document emphasizes that slope represents the rate of change between any two points and can be used to show proportional relationships between quantities in real-world scenarios.

1. Course 2, Lesson 1-8
1. The table shows the number of miles Greg walked during a walk-a-thon.
Find the constant rate of change for the table.
2. The graph represents the number of patients
that can be seen in a doctor’s office based on
the number of nurses on duty. Find the constant
rate of change for the graph.
3. Use the information in the table to find the rate of change.
Time (h) 1 2 3
Distance (mi) 4 8 12

2. Course 2, Lesson 1-8
ANSWERS
1. 4 miles per hour
2. 5 patients per nurse
3. 3 slices per student

3. HOW can you show that
two objects are proportional?
Ratios and Proportional Relationships
Course 2, Lesson 1-8

4. Ratios and Proportional Relationships
Course 2, Lesson 1-8 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
• 7.RP.2
Recognize and represent proportional relationships between quantities.
• 7.RP.2b
Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional relationships.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. • To find the slope of a line
• To interpret what the slope of a
line represents
Ratios and Proportional Relationships
Course 2, Lesson 1-8

6. Ratios and Proportional Relationships
Course 2, Lesson 1-8
slope = rise
run

7. Ratios and Proportional Relationships
Course 2, Lesson 1-8
Slope is the rate of change between any two points on a line.
slope = vertical change
horizontal change
= or 2
c
c
h
ha
an
nge
ge
in
in
y
x
2
1

8. 1
Need Another Example?
2 Definition of slope
3
4
Use (3, 15) and (5, 25).
seconds
5
6
Simplify.
Step-by-Step Example
1. The table below shows the relationship between the number of seconds y it
takes to hear thunder after a lightning strike and the miles x you are from the
lightning. Graph the data and find the slope. Explain what the slope represents.
miles
So, for every 5 seconds between a lightning flash and the sound
of thunder, there is 1 mile between you and the lightning strike.

9. Answer
Need Another Example?
The table below shows the relationship
between the number of hours Carlos works
and the amount of money that he earns.
Graph the data. Then find the slope of the
line. Explain what the slope represents.
The slope of the graph is
15 and represents the
amount earned per hour.

10. 1
Need Another Example?
Step-by-Step Example
2. Renaldo opened a savings
account. Each week he deposits
$300. Draw a graph of the
account balance versus time.
Find the numerical value of the
slope and interpret it in words.
The slope of the line is the rate at which the
account balance rises, or .

11. Answer
Need Another Example?
Nina drains a 20-gallon aquarium at a rate of
0.5 gallon per minute. Draw a graph of the
water in the aquarium over time. Find the
numerical value of the slope and interpret it
in words.
;
the slope is the
rate at which the
water in the tank
drains.

12. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-8
Ratios and Proportional Relationships

13. How did what you learned
today help you answer the
HOW can you show that
two objects are proportional?
Course 2, Lesson 1-8
Ratios and Proportional Relationships
Sample answers:
• By using slope to find the rate of change between two
points on a line
• By interpret the numerical value of a slope in the
context of a real-world situation

14. Give an example of
how being able to find
the constant rate of
change helped you with
today’s lesson on
finding slope.
Ratios and Proportional RelationshipsRatios and Proportional Relationships
Course 2, Lesson 1-8