For the direct variation equation y=2 2/3x , what is the constant of proportionality?(1 point) Responses 23 Start Fraction 2 over 3 End Fraction 2 2 3 3 223
The constant of proportionality in the direct variation equation y = 2 2/3x is 2 2/3, which can also be written as 8/3.
To find the constant of proportionality in a direct variation equation, we need to look at the coefficient of x. In the given equation y = 2 2/3x, the coefficient of x is 2 2/3.
To convert the mixed number 2 2/3 to an improper fraction, we multiply the whole number (2) by the denominator (3), then add the numerator (2) to get the new numerator. The denominator remains the same.
2 2/3 = (2 * 3 + 2) / 3 = 6/3 + 2/3 = 8/3
Therefore, the constant of proportionality is 8/3.
In a direct variation equation of the form y = kx, where y and x are variables and k is the constant of proportionality, the value of k can be found by comparing the equation to its standard form.
In the given equation, y = 2 2/3x, we can rewrite the fraction 2/3 as a decimal by dividing 2 by 3, which gives us approximately 0.6667.
Comparing the equation to the standard form y = kx, we can see that k is equal to 0.6667.
So, the constant of proportionality in this direct variation equation is 0.6667 (or approximately 2/3).