For what value of \(k \) does the line represented by the equation \(1-kx = -3y\) contain the point \((4,-3) \)?
Let's plug in the point \((4,-3)\) into the equation. We get \(1-4k = -3 \cdot (-3) \) so \(\boxed{k = -2}\).
If you want, you can put \(-2\) as k back into the equation, and see that it works.