To determine the constant of proportionality between $a$ and $b$, you divide $b$ by $a$ for any pair of corresponding values from the table. Let's calculate this:

1. From the first row:
   $\text{Constant of proportionality} = \frac{b}{a} = \frac{80}{10} = 8$

2. From the second row:
   $\frac{b}{a} = \frac{88}{11} = 8$

3. From the third row:
   $\frac{b}{a} = \frac{48}{6} = 8$

4. From the fourth row (fractional values):
   $\frac{b}{a} = \frac{1.60}{\frac{1}{5}} = \frac{1.60 \times 5}{1} = 8$

In each case, the constant of proportionality is $\mathbf{8}$.

Final Answer:

The constant of proportionality is 8.

Would you like a deeper explanation or help with anything else? Here are some related questions for practice:

1. How would you calculate the constant of proportionality for inverse relationships?
2. What does it mean if the constant of proportionality is less than 1?
3. How can proportionality constants be applied in real-life situations?
4. Can you graph the proportional relationship between $a$ and $b$?
5. How does the proportional relationship relate to linear equations?

Tip: To check your work, pick another row and recalculate $b \div a$. It should always yield the same constant!