for the direct variation equation Y = 2 2/3r, what is the constant of proportionality?
The constant of proportionality can be determined by observing the relationship between the variables in the direct variation equation.
In the equation Y = (8/3)r, the constant of proportionality is the coefficient in front of the variable r, which is 8/3.
To find the constant of proportionality in a direct variation equation, you can compare the equation to the standard form y = kx, where k represents the constant of proportionality.
In the given equation Y = 2 2/3r, we can rewrite it as Y = 8/3r.
Comparing this equation to the standard form, we can see that the constant of proportionality, k, is equal to 8/3.
In the direct variation equation Y = (2 2/3)r, the constant of proportionality represents the ratio between the dependent variable Y and the independent variable r. To determine the constant of proportionality, we need to rewrite the equation in the form of Y = k*r, where k represents the constant of proportionality.
Let's start by converting the mixed number (2 2/3) to an improper fraction. To do this, we multiply the whole number (2) by the denominator of the fraction (3), then add the numerator (2), and place the sum over the original denominator (3). So (2 2/3) can be written as (6/3 + 2/3), which simplifies to 8/3.
Now we have Y = (8/3)*r. Comparing this form to Y = k*r, we can see that the constant of proportionality (k) is equal to 8/3.
Therefore, the constant of proportionality for the direct variation equation Y = (2 2/3)r is 8/3.