[tex]equation \: of \: required \: line \implies[/tex]
[tex]4x + 3y + k = 0-----(1)[/tex]
[tex]since \: it \: passes \: through \: ( - 3,1),[/tex]
[tex] - 12 + 3 + k = 0[/tex]
[tex]k = 9[/tex]
[tex]substituting \: in \: k = 9 \: in \: (1),[/tex]
we get,
[tex]4x + 3y + 9 = 0[/tex]
[tex]hence \: the \: equation \: of \: the \: line \implies[/tex]
[tex] \red{ \boxed{ \bold{4x + 3y + 9 = 0}}}[/tex]
