Question

It is known that the point P(-9,18) belongs to the graph of the function y=k/x. Find k.

Answer 1

`k = (-162)`.

Explanation:

A point of the form
`(x_(0),\, y_(0))` belongs to the graph of this function,
`y = k / x`, if and only if the equation of this function holds after substituting in
`x = x_(0)` and
`y = y_(0)`.

The question states that the point
`(-9,\, 18)` belongs to the graph of this function. Thus, the equation of this function,
`y = k / x`, should hold after substituting in
`x = (-9)` and
`y = 18`:

`y = k / x`.

`18 = k / (-9)`.

Solve this equation for the constant
`k`:

`\begin{aligned}k &= 18 * (-9) \\ &= (-162)\end{aligned}`.

Thus,
`k = (-162)`.