Graph Proportional Relationships Splash Screen Graph Proportional Relationships

Graph Proportional Relationships Splash Screen Graph Proportional Relationships

Graph Proportional Relationships 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

Graph Proportional Relationships • 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

Graph Proportional Relationships

Graph Proportional Relationships 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).

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

Graph Proportional Relationships 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.

Graph Proportional Relationships Determine which situation represents a nonproportional relationship. A. B. Time (h) Height (cm) 5 0 20 2 10 1 18 3 15 2 16 4 20 3 14 Gallons Distance (mi) Soap (m. L) Water (L) 1 25 3 2 2 50 6 4 3 75 9 6 4 100 12 8 Time (s) Distance (m) 1 C. D.

Graph Proportional Relationships 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) 0 1 2 3 4 5 6 Height (ft) 140 120 100 80 60 40 20

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

Graph Proportional Relationships 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.

Graph Proportional Relationships 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 $3. 00. The cost of 2, 3, and 4 pounds of coffee respectively are $6, $9, and $12.

Graph Proportional Relationships 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 0 seconds and 0 rotations. The point (5, 2) represents 2 rotations in 5 seconds.

Graph Proportional Relationships 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)

Graph Proportional Relationships End of the Lesson