Answer
$y=\frac{1}{2}x-6$.
Work Step by Step
Want: Perpendicular to the line $2x+y=3$ and a y-intercept that is $\left( 0,-6 \right)$.
Solve further.
$\begin{align}
& 2x+y=3 \\
& y=-2x+3
\end{align}$
Slope of the provided line is $-2$ and the product of the slope of the lines perpendicular to each other results equal to $-1$. That is,
$\begin{align}
& -2\cdot m=-1 \\
& m=\frac{1}{2}
\end{align}$
Slope of the required line is $m=\frac{1}{2}$.
Put the provided values in the straight line equation.
$y=\frac{1}{2}x-6$
