Question

Suppose that y varies inversely with x. Given x =-3 when y = 8. Find Y when x = 4.

Answer 1

when x = 4, y = - 6

Explanation:

First, the expression for the statement y varies inversely with x, can be written as:

y ∝
`(1)/(x)`, and this can also be written in an equation form as:
`y = (k)/(x)`

where k = proportionality constant relating x and y.

Next we are told that: x =-3 when y = 8. and this can be written as:

`8 = (k)/(-3)`

finding the value of k, we cross-multiply to obtain the following:

k = -3 × 8 = -24

Finally, finding y when x = 4;

`y = (k)/(x)`

`y = (k)/(4)` where k = -24

∴
`y = (-24)/(4)`

`y = -6`

Therefore, when x = 4, y = - 6