By cross augmentation

\[\text{ }k\text{ }+\text{ }5\text{ }=\text{ }1\text{ }+\text{ }k\]

We get

\[2k\text{ }=\text{ }4\]

\[k\text{ }=\text{ }2\]

Henceforth, the line joining the focuses (- 1, 1) and (5, 7) is separated by the line \[x\text{ }+\text{ }y\text{ }=\text{ }4\] in the proportion 1: 2.