https://file.aiquickdraw.com/mathbot/file/1727293906726l9ntx424.jpg

The image shows three questions. Let's address them one by one:

### Question 19:
**"Tim biked \( \frac{2}{3} \) of an hour and traveled 4 miles. Find his average speed."**

To find Tim's average speed, we use the formula for speed:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

Here:
- Distance = 4 miles
- Time = \( \frac{2}{3} \) hours

Now, calculating speed:
\[
\text{Speed} = \frac{4}{\frac{2}{3}} = 4 \times \frac{3}{2} = 6 \text{ miles per hour}
\]

So, Tim's average speed is **6 miles per hour**.

### Question E:
This question asks to **state two coordinates that must be on the graph for it to be proportional**.

When a graph represents a proportional relationship, two points are always present:
1. \( (0, 0) \), because in a proportional relationship, when the input (x) is 0, the output (y) must also be 0.
2. Another point depends on the specific proportionality constant of the relationship, but commonly \( (1, k) \), where \( k \) is the constant of proportionality, will be on the graph.

Thus, the two coordinates that must be on the graph are:
- \( (0, 0) \)
- \( (1, k) \) where \( k \) is the constant of proportionality.

### Question 20:
This question asks to **find the constant of proportionality for three given relationships**. However, the image does not show the three relationships, so I cannot calculate the constants without that information. If you can provide the missing data, I'll help with that as well.

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Let me know if you'd like more details or clarifications! Here are five related questions to deepen your understanding:

1. How is the unit rate derived from a proportional relationship?
2. What happens if a point other than \( (0, 0) \) or \( (1, k) \) is included in a proportional graph?
3. What is the significance of the slope in the context of proportional relationships?
4. How can we determine if a relationship is proportional just by looking at its graph?
5. How can a proportionality constant help predict future values in a real-life scenario?

**Tip:** In a proportional relationship, the ratio between two quantities is always constant, and this constant represents the slope of the line when graphed.

Tim biked 2/3 of an hour and traveled 4 miles. Find his average speed. State two coordinates that must be on the graph for it to be proportional. Find the constant of proportionality for three given relationships.

Learn how to calculate Tim's average speed when he biked 4 miles in 2/3 of an hour. Explore proportional relationships and the constant of proportionality through examples of graph points and relationships. Suitable for Grades 6-8.

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