For the direct variation equation y = 2 2/3 * x_{i} what is the constant of proportionality? (1 point)
2 2/3
2/3
O 3
02
The constant of proportionality in the direct variation equation y = k*x is represented by k.
In the given equation y = 2 2/3 * x, the constant of proportionality is 2 2/3.
To find the constant of proportionality in a direct variation equation, we need to isolate the variable on one side of the equation.
The direct variation equation given is:
y = 2 2/3 * x_{i}
To isolate x_{i}, we need to divide both sides of the equation by 2 2/3:
y / 2 2/3 = x_{i}
To simplify the division, we convert the mixed number 2 2/3 to an improper fraction:
2 2/3 = (3 * 2 + 2) / 3 = 8/3
Substituting this value into the equation:
y / (8/3) = x_{i}
To divide by a fraction, we multiply by its reciprocal:
y * (3/8) = x_{i}
Therefore, the constant of proportionality is:
3/8
So, the correct answer is:
2/3
To find the constant of proportionality in a direct variation equation, you need to compare the ratios of the variables involved.
In the given equation, y = 2 2/3 * x_{i}, you can rewrite 2 2/3 as a fraction. It can be expressed as 8/3 since 2 is equivalent to 6/3 and adding 6/3 + 2/3 equals 8/3.
Now, if you compare the ratio of y to x_{i}, you'll see that y is equal to (8/3) * x_{i}. Since the coefficient in front of x_{i} is the constant of proportionality, in this case, it is 8/3.
Therefore, the constant of proportionality for the given equation is 8/3.