Answer:
[tex]y=\frac{24}{x}[/tex]
Step-by-step explanation:
We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of variation.
Upon substituting [tex]y=12[/tex] and [tex]x=2[/tex] in above equation, we will get:
[tex]12=\frac{k}{2}[/tex]
Let us solve for constant of variation.
[tex]12\cdot 2=\frac{k}{2}\cdot 2[/tex]
[tex]24=k[/tex]
Now, we will substitute [tex]k=12[/tex] in inversely proportion equation as:
[tex]y=\frac{24}{x}[/tex]
Therefore, the formula for the given scenario would be [tex]y=\frac{24}{x}[/tex].
