Final answer:
The constant of variation k is found to be 12 using the given values of a and b. With k determined, a is calculated to be 6 when b equals 2, illustrating the inverse variation between a and b.
Step-by-step explanation:
When it's stated that a varies inversely as b, this relationship can be expressed with the equation a = k/b, where k is the constant of variation. To find the value of k, you use the given values of a and b. Given that a=4 when b=3, you can substitute these values into the equation to get 4 = k/3. Multiplying both sides by 3 gives k = 12.
Now that we have k, we can solve for a when b=2. Substituting these values into the inverse variation equation we get a = 12/2 = 6. So, a = 6 when b=2.