To solve this 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 k such that:
y = kx
From the information given, we know that when x is 72, y is 6. We can use this information to find the value of k:
6 = k * 72
To find k, we simply divide both sides by 72:
k = 6 / 72
Calculating this gives:
k = 1 / 12
Now that we have the value of k, we can use it to find the value of y when x is 8. We plug x = 8 into the equation:
y = (1 / 12) * 8
This simplifies to:
y = 8 / 12
y = 2 / 3
Therefore, when x is 8, the value of y is 2/3.