Question

Two lines are represented by equations: −4x + 12y = 21 and y = kx – 12.What value of k will make lines parallel?

Answer 1

The parallel have equal slope.

Determine the slope of line -4x + 12y = 21.

`\begin{gathered} -4x+12y=21 \\ 12y=4x+21 \\ y=(4)/(12)x+(21)/(12) \\ =(1)/(3)x+(7)/(4) \end{gathered}`

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,

`k=(1)/(3)`