For the direct variation equation y=2 2/3x

Question

, what is the constant of proportionality?(1 point)
Responses

223
2 Start Fraction 2 over 3 End Fraction

23
Start Fraction 2 over 3 End Fraction

3
3

2

Answer 1

In the equation for direct variation $y=kx$, where $k$ is the constant of proportionality, your equation is given as $y=2\frac{2}{3}x$.

To find the constant of proportionality, we need to express $2\frac{2}{3}$ as an improper fraction:

$$2\frac{2}{3}=\frac{2\times 3+2}{3}=\frac{6+2}{3}=\frac{8}{3}$$

So, the constant of proportionality $k$ is $\frac{8}{3}$.

Since this value is not listed among the provided responses (which include $223,2\frac{2}{3},23,\frac{2}{3},3,2$), it seems there is either a misunderstanding or misrepresentation of the equation itself.

However, if you are asking for the specific form $2\frac{2}{3}$ rather than its value as an improper fraction, the answer would simply be $2\frac{2}{3}$.

Therefore, the constant of proportionality in improper fraction form is $\frac{8}{3}$, but if referring directly to the fractional form of the coefficient in the given equation, the answer is $2\frac{2}{3}$.