Answer
The slope-intercept equation is $y=-2x+1$.
Work Step by Step
It is known that the slope of the parallel lines is equal.
Thus, the slope of the required line will be equal to the slope of the line parallel to it, which is given by $2x+y-6=0$,
Therefore, to calculate the slope of the line, we rewrite it as: $-2x+6=y$
To calculate the derivative,
$\begin{align}
& y=-2x+6 \\
& m=-2 \\
\end{align}$
Thus the value of the slope is $-2$.
The slope-intercept form of the equation is given by $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$ and the point is $\left( 2,-3 \right)$
Substitute the values in the above formula,
$\begin{align}
& y-{{y}_{1}}=m\left( x-{{x}_{1}} \right) \\
& y+3=-2\left( x-2 \right) \\
& y+3=-2x+4 \\
& y=-2x+1
\end{align}$
Hence, the slope-intercept equation is $y=-2x+1$.
