# Lesson 12Using Graphs to Compare Relationships

Let’s graph more than one relationship on the same grid.

### Learning Targets:

• I can compare two related proportional relationships based on their graphs.
• I know that the steeper graph of two proportional relationships has a larger constant of proportionality.

## 12.1Number Talk: Fraction Multiplication and Division

Find each product or quotient mentally.

## 12.2Race to the Bumper Cars

Diego, Lin, and Mai went from the ticket booth to the bumper cars. Descriptions and tables representing their journeys are below.

1. Read each description and complete each table.

• Diego left the ticket booth at the same time as Tyler. Diego jogged ahead at a steady pace and reached the bumper cars in 30 seconds.
• Lin left the ticket booth at the same time as Tyler. She ran at a steady pace and arrived at the bumper cars in 20 seconds.
• Mai left the booth 10 seconds later than Tyler. Her steady jog enabled her to catch up with Tyler just as he arrived at the bumper cars.
Diego's time (seconds) Diego's distance (meters)
0
15
30 50
1
Lin's time (seconds) Lin's distance (meters)
0
25
20 50
1
Mai's time (seconds) Mai's distance (meters)
0
25
40 50
1

2. Draw a graph for each person’s journey, including Tyler's (from before).

• Drag the names to the correct lines to label them.
• If you choose to, you can use the Paint Brush tool to change the color of each line. Select the tool, click on a color in the palette below the graph, and then click on a line. Click on the Move tool (the arrow) before changing to a new paint brush color.
• You can hide any points you create with the checkbox below the graph.

3. For Tyler, Diego, and Lin, which person is moving the most quickly? How is that reflected in the graph?

### Are you ready for more?

Write equations to represent each person’s relationship between time and distance.

## 12.3Space Rocks and the Price of Rope

1. Meteoroid Perseid 245 and an unknown asteroid were traveling through the solar system.

Explore the applet to learn about the distance they had each traveled after a given time.

Is Asteroid x traveling faster or slower than Perseid 245? Explain how you know.

2. The graph shows the price, , of different lengths, , of two types of rope.

## Lesson 12 Practice Problems

1. Match each equation to its graph.

1

2

3

4

5

6

2. The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollars) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces).

__________________ vs volume

_____________________ vs volume

1. Which graph is which? Give them the correct titles.
2. Which quantities appear to be in a proportional relationship? Explain how you know.
3. For the proportional relationship, find the constant of proportionality. What does that number mean?
3. Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes.

1. Draw a graph with two lines that represent the bike rides of Lin and Andre.
2. For each line, highlight the point with coordinates and find .
3. Who was biking faster?
The passage contains multiple sections with descriptions of scenarios and tasks, including tables to complete, graphs to draw, and questions to answer. It also includes a few specific mathematical questions and tasks, such as determining who is moving the most quickly and finding the constant of proportionality.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Lesson 12Using Graphs to Compare Relationships

Let’s graph more than one relationship on the same grid.

### Learning Targets:

• I can compare two related proportional relationships based on their graphs.
• I know that the steeper graph of two proportional relationships has a larger constant of proportionality.

## 12.1Number Talk: Fraction Multiplication and Division

Find each product or quotient mentally.

## 12.2Race to the Bumper Cars

Diego, Lin, and Mai went from the ticket booth to the bumper cars. Descriptions and tables representing their journeys are below.

1. Read each description and complete each table.

• Diego left the ticket booth at the same time as Tyler. Diego jogged ahead at a steady pace and reached the bumper cars in 30 seconds.
• Lin left the ticket booth at the same time as Tyler. She ran at a steady pace and arrived at the bumper cars in 20 seconds.
• Mai left the booth 10 seconds later than Tyler. Her steady jog enabled her to catch up with Tyler just as he arrived at the bumper cars.
Diego's time (seconds) Diego's distance (meters)
0
15
30 50
1
Lin's time (seconds) Lin's distance (meters)
0
25
20 50
1
Mai's time (seconds) Mai's distance (meters)
0
25
40 50
1

2. Draw a graph for each person’s journey, including Tyler's (from before).

• Drag the names to the correct lines to label them.
• If you choose to, you can use the Paint Brush tool to change the color of each line. Select the tool, click on a color in the palette below the graph, and then click on a line. Click on the Move tool (the arrow) before changing to a new paint brush color.
• You can hide any points you create with the checkbox below the graph.

3. For Tyler, Diego, and Lin, which person is moving the most quickly? How is that reflected in the graph?

### Are you ready for more?

Write equations to represent each person’s relationship between time and distance.

## 12.3Space Rocks and the Price of Rope

1. Meteoroid Perseid 245 and an unknown asteroid were traveling through the solar system.

Explore the applet to learn about the distance they had each traveled after a given time.

Is Asteroid x traveling faster or slower than Perseid 245? Explain how you know.

2. The graph shows the price, , of different lengths, , of two types of rope.

## Lesson 12 Practice Problems

1. Match each equation to its graph.

1

2

3

4

5

6

2. The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollars) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces).

__________________ vs volume

_____________________ vs volume

1. Which graph is which? Give them the correct titles.
2. Which quantities appear to be in a proportional relationship? Explain how you know.
3. For the proportional relationship, find the constant of proportionality. What does that number mean?
3. Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes.

1. Draw a graph with two lines that represent the bike rides of Lin and Andre.
2. For each line, highlight the point with coordinates and find .
3. Who was biking faster?
user
The passage contains multiple sections with descriptions of scenarios and tasks, including tables to complete, graphs to draw, and questions to answer. It also includes a few specific mathematical questions and tasks, such as determining who is moving the most quickly and finding the constant of proportionality.

TYPE: MULTIPLE_QUESTIONS