If y varies inversely as x and y = 3 when x = 4, find y when x = 6.

To solve this problem, we can use the inverse variation formula, which states that y varies inversely as x can be represented as y = k/x, where k is the constant of variation.

Step 1: Find the value of k. Given that y = 3 when x = 4, we can substitute these values into the inverse variation formula: 3 = k/4

To find the value of k, we can cross multiply: 3 * 4 = k 12 = k

So, the constant of variation is k = 12.

Step 2: Find y when x = 6. Now that we have the value of k, we can use the inverse variation formula to find y when x = 6: y = k/x y = 12/6 y = 2

Therefore, when x = 6, y = 2.