Question

what is the constant of proportionality for the relationship shown in this table?
x: 2, 4, 6, 8
y: 1, 2, 3, 4
options: $\frac{1}{2}$, 2, 4, 8

Explanation:

Step1: Recall proportionality formula

For a proportional relationship $y = kx$, where $k$ is the constant of proportionality, we can solve for $k$ as $k = \frac{y}{x}$.

Step2: Calculate k using first table values

Use $x=2$, $y=1$:
$k = \frac{1}{2}$

Step3: Verify with other values

Check $x=4$, $y=2$: $k = \frac{2}{4} = \frac{1}{2}$;
Check $x=6$, $y=3$: $k = \frac{3}{6} = \frac{1}{2}$;
Check $x=8$, $y=4$: $k = \frac{4}{8} = \frac{1}{2}$.
All values confirm the same constant.

Answer:

$\frac{1}{2}$