For the direct variation equation y = 2 2/3 * x what is the constant of proportionality? Show your work.
A. 2
B. 2 2/3
C. 3
D. 2/3
To find the constant of proportionality in the direct variation equation y = kx, where k is the constant of proportionality, we can compare the given equation y = 2 2/3 * x to the standard form y = kx.
We can see that k = 2 2/3.
Therefore, the constant of proportionality is B. 2 2/3.
To find the constant of proportionality in the direct variation equation y = (2 2/3) * x, we need to divide both sides of the equation by x.
y / x = (2 2/3) * x / x
The x's on the right-hand side cancel out, leaving us with:
y / x = 2 2/3
Now, the constant of proportionality is the coefficient of x, which can be found by converting the mixed number 2 2/3 to an improper fraction.
To convert the mixed number 2 2/3 to an improper fraction, we multiply the whole number part (2) by the denominator (3) and add the numerator (2), then put the result over the denominator:
2 (3) + 2 = 6 + 2 = 8
So, 2 2/3 as an improper fraction is 8/3.
Therefore, the constant of proportionality in the equation is 8/3.
However, none of the options provided matches 8/3. Therefore, none of the options A, B, C, or D is correct.
To find the constant of proportionality in a direct variation equation, you need to isolate it by manipulating the equation.
The given equation is y = 2 2/3 * x.
First, rewrite the mixed number as an improper fraction: 2 2/3 = (2 * 3 + 2) / 3 = 8/3.
Now we have the equation y = 8/3 * x.
Since y is directly proportional to x, we can write this equation in the form y = kx, where k is the constant of proportionality.
Comparing this with our equation, we can see that k = 8/3.
So the constant of proportionality is 8/3.
Therefore, the answer is not listed among the options provided.