The slope of the given line is:
[tex]s=-\frac{8}{3}\text{.}[/tex]Therefore, the slope of a parallel line to the given line must be -8/3.
Using the slope-point formula for the equation of a line we get:
[tex]y-(-1)=-\frac{8}{3}(x-6)\text{.}[/tex]Taking the above equation to its standard form we get:
[tex]\begin{gathered} y+1=-\frac{8}{3}(x-6), \\ 3y+3=-8(x-6), \\ 3y+3=-8x+48, \\ 8x+3y=48-3, \\ 8x+3y=45. \end{gathered}[/tex]Answer: Option C.
