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
3
3
223
2 Start Fraction 2 over 3 End Fraction
2
The constant of proportionality for the direct variation equation y = (2/3)x is 2/3.
To find the constant of proportionality in a direct variation equation, you need to look at the coefficient of the independent variable.
In the equation y = 2 2/3x, the coefficient of x is 2 2/3.
To convert this mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. So, 2 * 3 + 2 = 6 + 2 = 8.
The improper fraction is 8/3, which means the constant of proportionality is 8/3.
Therefore, the correct answer is: Start Fraction 8 over 3 End Fraction.
To find the constant of proportionality for a direct variation equation, you need to compare the ratios of the variables involved. In this case, the equation is given as y = (2 2/3)x.
We can rewrite the equation as a fraction: y = 8/3x.
Now, compare the ratios: y/x = (8/3x) / x.
Simplify the expression: y/x = (8/3).
So, the constant of proportionality is 8/3, which is equivalent to 2 2/3.
Therefore, the correct answer is: Start Fraction 2 over 3 End Fraction.