To solve the problem, we start by understanding the concept of direct variation. When we say that y varies directly as x, it means that there is a constant ratio between y and x. This relationship can be expressed mathematically as:
y = kx
Where k is the constant of variation. To find the value of k, we can use the initial given values of y and x.
Given:
- y = 6
- x = 72
Substituting these values into the direct variation equation:
6 = k * 72
To isolate k, we divide both sides by 72:
k = \frac{6}{72} = \frac{1}{12}
Now that we have the value of our constant k, we can use it to find the value of y when x is 8. We substitute x = 8 into the direct variation equation:
y = kx
Substituting for k:
y = \frac{1}{12} * 8
Now, we can calculate:
y = \frac{8}{12} = \frac{2}{3}
Thus, the value of y when x is 8 is:
y = \frac{2}{3}
In summary, when x is 8, the value of y is two-thirds (or approximately 0.67).