1. Graph Proportional Relationships
Splash Screen
Graph Proportional Relationships

2. Main Idea and New Vocabulary Key Concept: Coordinate Plane
Example 1: Real-World Example: Identify Proportional Relationships
Example 2: Real-World Example: Identify Proportional Relationships
Example 3: Real-World Example: Identify Unit Rates
Lesson Menu

3. Identify proportional or nonproportional relationships by graphing on the coordinate plane.
ordered pair
coordinate plane
x-coordinate
y-coordinate
origin
y-axis
x-axis
quadrants
Main Idea/Vocabulary

4. Key Concept

5. Identify Proportional Relationships
RIDES The table shows the number of seconds and the number of times a ride at an amusement park rotates. Determine whether the number of rotations is proportional to the number of seconds by graphing on the coordinate plane. Explain your reasoning.
Step 1 Write the two quantities as ordered pairs (number of seconds, number of rotations) The ordered pairs are (0, 0), (5, 2), (10, 5), and (15, 10).
Example 1

6. Identify Proportional Relationships
Step 2 Graph the ordered pairs on the coordinate plane. Then connect the ordered pairs.
Example 1

7. Identify Proportional Relationships
Step 3 Determine if the two quantities show a proportional relationship by looking at the graph.
Answer:
The number of rotations is not proportional to the number of seconds because the graph is not a straight line.
Example 1

8. Determine which situation represents a nonproportional relationship.
Time (h)
Height (cm) 20 1 18 2 16 3 14 A. B.
Time (s)
Distance (m) 1 5 2 10 3 15 4 20 C. D.
Gallons
Distance (mi) 1 25 2 50 3 75 4
100
Soap (mL)
Water (L) 3 2 6 4 9 12 8
Example 1 CYP

9. Identify Proportional Relationships
HOT AIR BALLOON A hot air balloon is at 140 feet and descends 20 feet per minute. Determine whether the height of the hot air balloon is proportional to the number of minutes. Explain your reasoning.
Step 1 Make a table to find the height after 0, 1, 2, 3, 4, 5, and 6 minutes.
Time (min) 1 2 3 4 5 6
Height (ft)
140
120
100 80 60 40 20
Example 2

10. Identify Proportional Relationships
Step 2 Graph the ordered pairs on the coordinate plane. Then connect the ordered pairs.
Example 2

11. Identify Proportional Relationships
Step 3 Determine if the two quantities show a proportional relationship by looking at the graph.
Answer:
The height of the hot air balloon is not proportional to the number of minutes because the graph does not pass through the origin.
Example 2

12. Determine which situation represents a proportional relationship.
A. A car traveled 50 miles in 1 hour, 70 miles in 2 hours, and 90 miles in 3 hours.
B. Admission to a park can be represented as the following ordered pairs (number of rides, cost): (1, 5.50), (2, 7), (3, 8.50), and (4, 10).
C. The height of a plant after 3, 6, and 9 days was 9, 12, and 18 millimeters, respectively.
D. A coffee shop sells 1 pound of coffee for $ The cost of 2, 3, and 4 pounds of coffee respectively are $6, $9, and $12.
Example 2 CYP

13. Identify Unit Rates
RIDES Refer to the graph in Additional Example 1. Explain what the points (0, 0) and (5, 2) represent.
Answer:
The point (0, 0) represents seconds and 0 rotations The point (5, 2) represents rotations in 5 seconds.
Example 3

14. SCOOTERS Refer to the graph at the right
SCOOTERS Refer to the graph at the right. Which of the following ordered pairs represents the unit rate?
A. (0, 0)
B. (1, 4)
C. (2, 8)
D. (3, 12)
Example 3 CYP

15. Graph Proportional Relationships
End of the Lesson