[tex]y=mx+b \\ \\
(x,y)=(-4,-5) \hbox{ and } (x,y)=(-6,3) \\ \Downarrow \\
-5=-4m+b \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \times (-3) \\
3=-6m+b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times 2 \\ \\
15=12m-3b \\
\underline{6=-12m+2b} \\
21=-b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-1) \\
\boxed{b=-21}[/tex]
The value of b is -21.
