Given y is inversely proportional to x If the difference in the values of y when x 2 and x 6 is 5 How do i find the value of y when x 4?

Answer 1

As y is inversely proportional to x, the equation relating x to y is given by:

y = k/x

where k is the constant of proportionality.

Using this we can find expressions for the value of y when x = 2 and x = 6 in terms of k:

x = 2 → y = k/2

x = 6 → y = k/6

The difference between these is k/2 - k/6 = 3k/6 - k/6 = 2k/6 = k/3

But this, we are told is 5; thus:

k/3 = 5

→ k = 15

Thus y = 15/x

Now that we have found the equation relating x to y, we can plug in the value for x = 4 and find the value of y:

The value for y when x = 4 is y = 15/4 = 3.75