Answer:
y = -8
Explanation:
When two variables vary inversely, their relation is proportional. This means that their product is constant.
We can show the constant of proportionality (k) using the equation:
x · y = k
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
Note: you may also see this written as:
y = k / x
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
↓ plugging in the given values
(-4) · 6 = k
-24 = k
k = -24
Using this constant, we now solve for y when x = 3 by plugging that value into the proportionality equation above:
x · y = k
↓ plugging in the known values
3 · y = -24
↓ dividing both sides by 3
y = -24/3
y = -8