Let's go through this step by step to solve the problem based on the table in the image:

The table presents data for shots made from the right $r$ and shots made from the left $f$, and we need to calculate the constant of proportionality and express the proportion between these quantities.

Step 1: Constant of Proportionality

The constant of proportionality $k$ can be found by dividing the number of shots made from the left $f$ by the number of shots made from the right $r$ for each pair of values. We want to check if the ratio $\frac{f}{r}$ is consistent across all rows.

Using the data in the table:

1. For A: $\frac{f}{r} = \frac{20}{28} = \frac{5}{7}$
2. For B: $\frac{f}{r} = \frac{30}{42} = \frac{5}{7}$
3. For C: $\frac{f}{r} = \frac{40}{56} = \frac{5}{7}$
4. For D: $\frac{f}{r} = \frac{45}{63} = \frac{5}{7}$

Since the ratio is consistent, the constant of proportionality $k$ is: $k = \frac{5}{7}$

Step 2: Proportion between the Quantities

To express the relationship as a proportion: $\frac{f}{r} = \frac{5}{7}$

This proportion shows that for every 7 shots made from the right, 5 shots are made from the left.

Summary:

• The constant of proportionality is $\frac{5}{7}$.
• The proportion showing the relationship is $\frac{f}{r} = \frac{5}{7}$.

Let me know if you need more details, and here are some related questions to deepen your understanding:

1. Can you find the number of shots from the left if 84 shots were made from the right?
2. How would the constant of proportionality change if the data in one row was altered?
3. What is the relationship between the two variables if the constant of proportionality were to be inverted (i.e., using $\frac{r}{f}$)?
4. How can you verify that the shots made from the left depend linearly on the shots made from the right?
5. How would the results change if the shots from the left and right were swapped in the table?

Tip: Always check whether ratios are consistent across data rows before concluding proportionality.