y varies inversely with x, and y = 10 when x = 2. What is the equation for the inverse variation?
xy=20
To find the equation for an inverse variation, we can use the formula:
y = k/x
Where k is the constant of variation. Given that y varies inversely with x, we can substitute the values of y and x into the equation:
10 = k/2
Now we just need to solve for k. Multiply both sides of the equation by 2 to isolate k:
20 = k
So the constant of variation is k = 20.
Substitute this value back into the equation for inverse variation:
y = 20/x