Question

If y varies inversely as x and y= -4 when x=2, find y when x= -6.

Answer 1

We are told that y varies inversely to x. This means that we have the following equation

`y=(k)/(x)`

where k is a constant. We are told that when x=2 we have y=-4. So we have the equation

`\text{ -4=}(k)/(2)`

Then, by multiplying both sides by 2, we get

`k=2\cdot(\text{ -4)= -8}`

So, we have the equation

`y=\frac{\text{ -8}}{x}`

So, when x= -6, we have that

`y=\frac{\text{ -8}}{\text{ -6}}=(8)/(6)=(4\cdot2)/(3\cdot2)=(4)/(3)`