At the beginning of every soccer practice, Coach Alex has the players warm up and stretch. They do 3 minutes of warm-up exercises for every 2 minutes of stretching.

Question

Complete the table.
Minutes of warm-ups 3 15
Minutes of stretching 2 4 6
Graph the data from the table.

Answer 1

To complete the table, we need to maintain the ratio of warm-up exercises to stretching, which is \(3\) minutes of warm-ups for every \(2\) minutes of stretching.

Completing the Table

1. For 3 minutes of warm-ups:

   • The corresponding stretching will be \(2\) minutes.

2. For 15 minutes of warm-ups:

   • We can calculate the stretching using the ratio: \[ \text{Stretching} = \left(\frac{2}{3}\right) \times 15 = 10 \text{ minutes} \]

So, your completed table is:

| Minutes of warm-ups | 3 | 15 | |---------------------|---|----| | Minutes of stretching| 2 | 10 |

Completed Table:

| Minutes of Warm-ups | 3 | 15 | |---------------------|---|----| | Minutes of Stretching | 2 | 10 |

Graphing the Data

To graph the data from the table, plot the pairs of (warm-ups, stretching) as points on a coordinate plane:

• Point 1: \( (3, 2) \)
• Point 2: \( (15, 10) \)

1. On the X-axis, plot the minutes of warm-ups.
2. On the Y-axis, plot the minutes of stretching.

You can use a graph with the following scale if you like:

• X-axis scale (Minutes of warm-ups): 0 to 20 (increments of 3)
• Y-axis scale (Minutes of stretching): 0 to 12 (increments of 2)

Graph Representation

1. Point (3, 2)
2. Point (15, 10)

Connect those points with a line to visualize the relationship, which in this case should be linear due to the proportionality.

Overall Summary:

• The relationship shown in the graph represents the constant ratio of stretching to warm-up minutes during the practice sessions.