Answer
The $y$ intercept of the line is $-3$.
Work Step by Step
Consider a line that passes through the point $\left( 2,-6 \right)$ and has a slope of $-\frac{3}{2}$.
Substitute $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 2,-6 \right)$ and $m=-\frac{3}{2}$ (the slope of the given line) in the equation:
$\begin{align}
& y-\left( -6 \right)=-\frac{3}{2}\left( x-2 \right) \\
& y+6=-\frac{3}{2}x+3
\end{align}$
Solve the above equation for $y$:
$\begin{align}
& y+6=-\frac{3}{2}x+3 \\
& y=-\frac{3}{2}x+3-6 \\
& y=-\frac{3}{2}x-3
\end{align}$
Compare the last equation with the slope–intercept form $y=mx+b$ of the equation of a line in slope intercept form
$b=-3$
Thus, the $y$ intercept of the given line is $b=-3$.
