If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
The correct answer is: y = \(\frac{2}{3}\)
Explanation:
The direct relation can be written as follows:
\(y \propto x\)
Now to remove the proportional sign, we use the constant of proportionality, let's say k, as follows:
\(y = kx\)
When y = 6, x = 72, k will be:
\(k =\frac{y}{x} \\ k =\frac{6}{72} = \frac{1}{12}\)
Now we know the value of k, let's find the value of y when x = 8:
\(y = kx \\ y =\frac{1}{12} * 8 =\frac{2}{3}\)
Hence the correct answer is: y = \(\frac{2}{3}\)