Question

On a rectangular hyperbola, if one point is (2, 3) and y varies inversely to x, find y when x is 6.

Answer 1

y = 1

Explanation:

y is inversely proportion to x means that ,

y ∝ 1/x or ,

`y\ \alpha\ (1)/(x)`

When we remove the proportionality sign we get,

`y=k((1)/(x))\\y=(k)/(x) \\`

now we know the point is (2 , 3) which means it corresponds to (x , y) which furthermore means y=3 when x=2,

so we insert these values and get the value of k.

`y=(k)/(x) \\\\3=(k)/(2)\\\\6=k\\`

now the equation becomes,

`y=(6)/(x)`

now we need to find y when x is 6 so just replace x with 6

`y=(6)/(x)\\\\y=(6)/(6) \\\\y=1`

so we get the value of y is 1