Question

the table of paired values represents a proportional relationship.

x	5	10	20	50
y	10	20	40	100

what is the constant of proportionality for the relationship?

enter your answer, in simplest form, in the box.

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

Step3: Verify with other pairs

For $x=10$, $y=20$: $k = \frac{20}{10} = 2$
For $x=20$, $y=40$: $k = \frac{40}{20} = 2$
For $x=50$, $y=100$: $k = \frac{100}{50} = 2$

Answer:

2