Suppose that $y$ is directly proportional to $x$. Find the constant of proportionality $\mathrm{k}$ if $\mathrm{y}=55.2$ when $\mathrm{x}=12$. \[ \mathrm{k}= \] (Write your answer as a decimal.) Using the $\mathrm{k}$ from above write the variation equation in terms of $x$. \[ y= \] Using the $\mathrm{k}$ from above find $\mathrm{y}$ given that $\mathrm{x}=14$. \[ y= \]

Step 1 ：Given that $y$ is directly proportional to $x$, we can write the equation as $y = kx$.

Step 2 ：Substitute the given values of $y = 55.2$ and $x = 12$ into the equation to find the constant of proportionality $k$.

Step 3 ：Rearrange the equation to $k = \frac{y}{x}$ and substitute the given values to get $k = \frac{55.2}{12}$.

Step 4 ：Calculate the value of $k$ to get $k \approx 4.6$.

Step 5 ：Substitute the value of $k$ into the equation $y = kx$ to get the variation equation in terms of $x$ as $y = 4.6x$.

Step 6 ：Given that $x = 14$, substitute $x$ into the equation $y = 4.6x$ to find the value of $y$.

Step 7 ：Calculate the value of $y$ to get $y \approx 64.4$.

Step 8 ：\(\boxed{k \approx 4.6}\)

Step 9 ：\(\boxed{y = 4.6x}\)

Step 10 ：\(\boxed{y \approx 64.4}\)