Question

1. the point ( p(2, 3) ) lies on the rational function with equation ( y = \frac{k}{x} ). find the value of ( k ), and find the equation of the rational function shown.

Explanation:

Step1: Substitute point into equation

Substitute $x=2$, $y=3$ into $y=\frac{k}{x}$:
$3=\frac{k}{2}$

Step2: Solve for k

Multiply both sides by 2:
$k=3\times2=6$

Step3: Write final equation

Substitute $k=6$ back into $y=\frac{k}{x}$:
$y=\frac{6}{x}$

Answer:

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