Find the variation constant and an equation of variation where y varies inversely as x and y=2 when x=6
y = k/x
2 = k/6
...
To find the variation constant and an equation of variation, we need to use the formula for inverse variation, which is y = k/x, where k is the variation constant.
Given that y varies inversely as x, we have y = k/x.
We are also given that when x = 6, y = 2. We can substitute these values into the equation to solve for k.
2 = k/6
To isolate k, we can cross-multiply:
2 * 6 = k
12 = k
So the variation constant, k, is 12.
Now we can write the equation of variation:
y = k/x
Substituting the value of k:
y = 12/x
Therefore, the variation constant is 12 and the equation of variation is y = 12/x.