Answer
The coefficient of $x$ is $1$ and the coefficient of $y$ is $-2$.
Work Step by Step
Let the coefficient of $x$ be $A$ and $y$ be $B$.
Now the equation can be written as,
$Ax+By-12=0$ (I)
To calculate the $y\ \text{intercept}$, substitute $x=0$ in equation (I); that is,
$\begin{align}
& A\times 0+By-12=0 \\
& By-12=0 \\
& By=12 \\
& y=\frac{12}{B}
\end{align}$
It is given that the $y\ \text{intercept}=-6$.
$\begin{align}
& -6=\frac{12}{B} \\
& B=\frac{12}{-6} \\
& =-2
\end{align}$
Now, we will rewrite the equation in the slope intercept form $y=mx+c$.
$\begin{align}
& By=-Ax+12 \\
& y=\frac{-A}{B}x+\frac{12}{B}
\end{align}$
This means that the slope is $\frac{-A}{B}$.
It is given that the $\text{slope}=\frac{1}{2}$. Substituting the value of B
$\begin{align}
& \frac{-A}{-2}=\frac{1}{2} \\
& \frac{-A}{-2}\left( 2 \right)=\frac{1}{2}\left( 2 \right) \\
& A=\frac{2}{2} \\
& A=1
\end{align}$
Hence, the coefficient of $x$ is 1 and the coefficient of $y$ is $-2$.
