Unit 5, Lesson 4
Comparing Relationships with Tables
Accelerated 6
Practice
Problem 1
Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?
- How loud a sound is
distance from
listener (ft)sound
level (dB)5 85 25 79 35 73 40 67 - The cost of fountain drinks at Hot Dog Hut.
volume
(fl oz)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 ($) |
|---|---|
| \(\frac{9}{10}\) | |
| 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 |
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 | \(7\frac12\) |
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 | |
| \(\frac12\) |