Question

graphs of proportional relationships ada math assessment 6. \\(\frac{x}{y} = 2\\) tell whether \\(x\\) and \\(y\\) are proportional. if so, identify the constant of proportionality. if not, leave the response box blank. constant of proportionality: options: yes, no, \\(k = 0\\), \\(k = \frac{1}{4}\\), \\(k = \frac{1}{3}\\), \\(k = \frac{1}{2}\\), \\(k = \frac{1}{5}\\)

Explanation:

Step1: Rewrite to proportional form

Rearrange the given equation to match $x=ky$.
Starting with $\frac{x}{y}=2$, multiply both sides by $y$:
$x = 2y$

Step2: Verify proportionality

The equation fits the proportional relationship form $x=ky$, where $k$ is the constant of proportionality.

Step1: Rearrange for y as dependent

Solve $\frac{x}{y}=2$ for $y$.
Multiply both sides by $y$, then divide by 2:
$y = \frac{1}{2}x$

Step2: Confirm proportionality

The equation matches $y=kx$, so $x$ and $y$ are proportional.

Answer:

1. Yes
2. $k=2$

(Note: Since 2 is not listed in the provided options, but mathematically the constant of proportionality for $x$ relative to $y$ is 2. If considering $y$ relative to $x$, rearranging gives $y=\frac{1}{2}x$, so $k=\frac{1}{2}$ for $y$ as the dependent variable. Based on standard proportionality definition where $x \propto y$, the constant is 2; if framing $y \propto x$, it is $\frac{1}{2}$.)

Corrected alignment with options: