Use the slope formula:
\(\displaystyle{m}=\frac{{{y}{2}-{y}{1}}}{{{x}{2}-{x}{1}}}\)

Substitute (x1,y1)=(-4,k),(x2,y2)=(6,-7), and m=\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}\)

\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}=\frac{{-{7}-{k}}}{{{6}-{\left(-{4}\right)}}}\)

\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}=\frac{{-{7}-{k}}}{{10}}\)

Multiply both sides by -10

\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}-{10}=\frac{{-{7}-{k}}}{{10}}\cdot{\left(-{10}\right)}\) 2=7+k -5=k k=-5

Substitute (x1,y1)=(-4,k),(x2,y2)=(6,-7), and m=\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}\)

\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}=\frac{{-{7}-{k}}}{{{6}-{\left(-{4}\right)}}}\)

\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}=\frac{{-{7}-{k}}}{{10}}\)

Multiply both sides by -10

\(\displaystyle-{\left(\frac{{1}}{{5}}\right)}-{10}=\frac{{-{7}-{k}}}{{10}}\cdot{\left(-{10}\right)}\) 2=7+k -5=k k=-5