Question

the table of paired values represents a proportional relationship.

x	2	5	6	8
y	10	25	30	40

what is the constant of proportionality for the relationship?

• $\frac{1}{2}$
• 2
• 5
• 10

Explanation:

Step1: Recall proportionality formula

For a proportional relationship, $y = kx$, where $k$ is the constant of proportionality. Rearranged, $k = \frac{y}{x}$.

Step2: Calculate k using first pair

Use $x=2$, $y=10$:
$k = \frac{10}{2} = 5$

Step3: Verify with other pairs

Check $x=5$, $y=25$: $k = \frac{25}{5} = 5$
Check $x=6$, $y=30$: $k = \frac{30}{6} = 5$
Check $x=8$, $y=40$: $k = \frac{40}{8} = 5$

Answer:

C. 5