For the direct variation equation y = 2 2/3x, what is the constant of proportionality?

1 answer

In the direct variation equation of the form \( y = kx \), the constant of proportionality is represented by \( k \).

In your case, the equation is given as:

\[ y = 2 \frac{2}{3} x \]

To convert \( 2 \frac{2}{3} \) to an improper fraction:

\[ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \]

Now, the equation can be rewritten as:

\[ y = \frac{8}{3} x \]

Thus, the constant of proportionality \( k \) is \( \frac{8}{3} \).