The variable $$ y $$ varies inversely with $$ x $$. Write an inverse variation equation that relates $$ x $$ and $$ y $$. Then find the missing value of $$ x $$ or $$ y $$. 19. When $$ x=6, y=2 $$. Find $$ x $$ when $$ y=1 $$.

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1. We are told that $$ y $$ varies inversely with $$ x $$, which means the relation can be written as  
   $$
   y = \frac{k}{x},
   $$
   where $$ k $$ is a constant.

2. Using the values $$ x = 6 $$ and $$ y = 2 $$, we can substitute into the equation to find $$ k $$:
   $$
   2 = \frac{k}{6}.
   $$
   Multiplying both sides by 6 gives:
   $$
   k = 12.
   $$

3. Now the inverse variation equation is:
   $$
   y = \frac{12}{x}.
   $$

4. To find $$ x $$ when $$ y = 1 $$, substitute $$ y = 1 $$ into the equation:
   $$
   1 = \frac{12}{x}.
   $$
   Multiply both sides by $$ x $$ to obtain:
   $$
   x = 12.
   $$

Thus, when $$ y = 1 $$, the value of $$ x $$ is $$ 12 $$.
The inverse variation equation is $$ y = \frac{12}{x} $$. When $$ y = 1 $$, $$ x = 12 $$.

The variable \( y \) varies inversely with \( x \). Write an inverse variation equation that relates \( x \) and \( y \). Then find the missing value of \( x \) or \( y \). 19. When \( x=6, y=2 \). Find \( x \) when \( y=1 \).

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