For the direct variation equation y=2 2/3x , what is the constant of proportionality
The constant of proportionality in the direct variation equation y = (2/3)x is 2/3.
In the direct variation equation y=2 2/3x, the constant of proportionality is the coefficient of x, which is 2 2/3.
To convert the mixed number 2 2/3 to a fraction, we multiply the whole number (2) by the denominator of the fraction (3) and add the numerator (2). This gives us 6 (2 × 3) + 2 = 8.
So, the mixed number 2 2/3 can be written as the improper fraction 8/3.
Therefore, in the direct variation equation y=2 2/3x, the constant of proportionality is 8/3.
In the direct variation equation y = kx, where y and x are variables and k is the constant of proportionality, we can determine the constant of proportionality by comparing the equation to its standard form.
For the given equation y = 2 2/3x, we can rewrite the number 2 2/3 as a mixed number or improper fraction.
2 2/3 = (2 * 3 + 2) / 3 = 8/3
Now, we can see that the equation is in the form y = (8/3)x. By comparing it to the standard form y = kx, we can determine that the constant of proportionality is k = 8/3.
Therefore, the constant of proportionality in the direct variation equation y = 2 2/3x is 8/3.