Final answer:
To find the value of y when x=12 for an inverse variation where x=2 when y=-4, use the equation xy=k to get k=-8. Then substitute x=12 into the equation to find y=-2/3.
Step-by-step explanation:
The question is asking for a value of y in an inverse variation where we know that when x=2, y=-4. An inverse variation can be represented by the equation xy=k, where k is a constant. To find k, we substitute the given values of x and y into the equation:
2(-4) = k
k = -8
Now we have the constant of variation and can find the value of y when x=12 using the equation:
(12)y = -8
y = -8/12
y = -2/3
Therefore, when x=12, the value of y in this inverse variation is -2/3.