for the direct variation equation Y = 2 2/3r, what is the constant of proportionality?
2 2/3
2/3
2
3
The constant of proportionality is 2 2/3.
To determine the constant of proportionality for the direct variation equation Y = 2 2/3r, we need to compare the given equation to the standard form of a direct variation equation, which is Y = kx, where k represents the constant of proportionality.
In this case, we can rewrite the equation Y = 2 2/3r as Y = 8/3r.
Now we can see that the coefficient of r is 8/3. Therefore, the constant of proportionality, k, is equal to 8/3.
So, the correct answer is 8/3.
To find the constant of proportionality in the direct variation equation Y = (2 2/3)r, we can rewrite the equation in the form of Y = kx, where k represents the constant of proportionality and x represents the variable.
In this case, the given equation is Y = (2 2/3)r. To simplify the mixed number 2 2/3, we can convert it to an improper fraction.
First, we multiply the whole number 2 by the denominator 3. This gives us 2 x 3 = 6. Next, we add the result to the numerator 2, giving us 6 + 2 = 8.
Now, we can rewrite the mixed number 2 2/3 as the improper fraction 8/3. The equation becomes Y = (8/3)r.
Comparing this equation to the general form Y = kx, we can see that the constant of proportionality, k, is equal to 8/3.
Therefore, the constant of proportionality in the direct variation equation Y = (2 2/3)r is 8/3.