Question

a linear relationship is shown in the table.
time (hours) | 2 | 4 | 6 | 8
distance (miles) | 8 | 16 | 24 | 32
is the linear relationship also proportional? explain.

• yes, the constant of proportionality is 4.
• yes, there is no constant of proportionality.
• no, the constant of proportionality is 4.
• no, there is no constant of proportionality.

Explanation:

Step1: Check proportionality ratio

Calculate $\frac{\text{Distance}}{\text{Time}}$ for each pair:
$\frac{8}{2}=4$, $\frac{16}{4}=4$, $\frac{24}{6}=4$, $\frac{32}{8}=4$

Step2: Verify constant ratio

All ratios equal 4, so a constant exists.

Step3: Confirm proportionality

A linear relationship with a constant $\frac{y}{x}$ ratio is proportional.

Answer:

Yes, the constant of proportionality is 4.