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

Answer:

y = 1

Step-by-step explanation:

y is inversely proportion to x means that ,

y ∝ 1/x or ,

$y\ \alpha\ \frac{1}{x}$

When we remove the proportionality sign we get,

$y=k(\frac{1}{x})\\y=\frac{k}{x}$

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.

$y=\frac{k}{x} \\\\3=\frac{k}{2}\\\\6=k$

now the equation becomes,

$y=\frac{6}{x}$

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

$y=\frac{6}{x}\\\\y=\frac{6}{6} \\\\y=1$

so we get the value of y is 1