The given line equation is,
[tex]3x-y=-6[/tex]
The given point is ,
[tex](5,1)[/tex]
The graph will look like this,
let us rewrite the line equtaion as ,
[tex]3x-y+6=0[/tex]
now, let us compare with the general equation of line,
[tex]Ax+By+C=0[/tex]
then, A= 3,B=-1 and c= 6.
let us use the formula,
[tex]\begin{gathered} d=\frac{|Ax+By+c|}{\sqrt[]{A^2+B^2}} \\ d=\frac{|3\times5+(-1)\times1+6|}{\sqrt[\square]{3^2+(-1)^2}} \\ d=\frac{|15-1+6|}{\sqrt[\square]{9+1}} \\ d=\frac{20}{\sqrt[\square]{10}} \\ d=6.32 \end{gathered}[/tex]
The shortest distance is 6.32 .
