The parallel have equal slope.
Determine the slope of line -4x + 12y = 21.
[tex]\begin{gathered} -4x+12y=21 \\ 12y=4x+21 \\ y=\frac{4}{12}x+\frac{21}{12} \\ =\frac{1}{3}x+\frac{7}{4} \end{gathered}[/tex]The slope of line -4x + 12 y = 21 is equal to m = 1/3.
The slope of line y = kx -12 is k.
For the lines to be parallel slope must be equal. So,
[tex]k=\frac{1}{3}[/tex]