Lesson 4

Comparing Relationships with Tables

Let’s explore how proportional relationships are different from other relationships.

Problem 1

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?

  1. How loud a sound is depending on how far away you are.
    distance to
    listener (ft)    		 sound
    level (dB)
    5 85
    10 79
    20 73
    40 67
  2. The cost of fountain drinks at Hot Dog Hut.
    volume
    (fluid ounces)    		 cost
    ($)
    16 $1.49
    20 $1.59
    30 $1.89

Problem 2

A taxi service charges $1.00 for the first \(\frac{1}{10}\) mile then $0.10 for each additional \(\frac{1}{10}\) mile after that.

Fill in the table with the missing information then determine if this relationship between distance traveled and price of the trip is a proportional relationship.

distance traveled (mi) price (dollars)
\(\frac{9}{10}\)
2
\(3\frac{1}{10}\)
10

 

Problem 3

A rabbit and turtle are in a race. Is the relationship between distance traveled and time proportional for either one? If so, write an equation that represents the relationship.

Turtle’s run:

distance (meters) time (minutes)
108 2
405 7.5
540 10
1,768.5 32.75

Rabbit’s run:

distance (meters) time (minutes)
800 1
900 5
1,107.5 20
1,524 32.5

Problem 4

For each table, answer: What is the constant of proportionality?

a b
2 14
5 35
9 63
\(\frac13\) \(\frac73\)
a b
3 360
5 600
8 960
12 1440
a b
75 3
200 8
1525 61
10 0.4
a b
4 10
6 15
22 55
3 \(7\frac12\)

 

(From Unit 5, Lesson 1.)

Problem 5

Here is a table that shows the ratio of flour to water in an art paste. Complete the table with values in equivalent ratios.

cups of flour cups of water
1 \(\frac12\)
4
3
\(\frac12\)
(From Unit 2, Lesson 9.)