Question

The variables x and y have a proportional relationship, and y=13 when x=34.

Which equation represents this relationship?
Responses

y=512x
y equals 5 over 12 end fraction x

y=14x
y equals 1 over 4 end fraction x

y=49x

Answer 1

Since \(x\) and \(y\) have a proportional relationship, we can express this relationship as \(y = kx\), where \(k\) is the constant of proportionality.

Given that \(y = 13\) when \(x = 34\), we can find \(k\) as follows:

\[
k = \frac{y}{x} = \frac{13}{34}
\]

Now we can write the equation that represents this relationship:

\[
y = \frac{13}{34}x
\]

Next, we should simplify this fraction. Dividing both the numerator and the denominator by 13:

\[
k = \frac{1}{\frac{34}{13}} = \frac{1}{2.61538461538} \approx 0.38
\]

However, we can keep the fraction as \(k = \frac{13}{34}\) for the exact representation.

Looking at the provided options:

- \(y = 512x\)
- \(y = \frac{5}{12} x\)
- \(y = 14x\)
- \(y = \frac{1}{4} x\)
- \(y = 49x\)

None of these options directly match \(y = \frac{13}{34}x\). Therefore, it seems there may be a misunderstanding in interpreting the question based on given responses.

Since you seek a proportional relationship, you could also check if any of the equations provided can equate to a similar scale to our constant \(\frac{13}{34}\).

However, the equation that suits the proportionality derived from the initial condition does not match any of the options given.

If these are the only responses available, then none of them represent the accurate proportional relationship based on the information given.