Answer:
[tex]k = (-162)[/tex].
Step-by-step explanation:
A point of the form [tex](x_{0},\, y_{0})[/tex] belongs to the graph of this function, [tex]y = k / x[/tex], if and only if the equation of this function holds after substituting in [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex].
The question states that the point [tex](-9,\, 18)[/tex] belongs to the graph of this function. Thus, the equation of this function, [tex]y = k / x[/tex], should hold after substituting in [tex]x = (-9)[/tex] and [tex]y = 18[/tex]:
[tex]y = k / x[/tex].
[tex]18 = k / (-9)[/tex].
Solve this equation for the constant [tex]k[/tex]:
[tex]\begin{aligned}k &= 18 \times (-9) \\ &= (-162)\end{aligned}[/tex].
Thus, [tex]k = (-162)[/tex].
