Use the point-slope form of a line: \(y-y_1=m(x-x_1)\)

where m is the slope and \((x_1\times y_1)\) is a point of the line.

Two lines are perpendicular if their slopes are negative reciprocals. Rewriting the given line, \(\displaystyle{5}{x}-{y}={2}\to{y}={5}{x}-{2}\), which has a slope of 5. So, the slope of the perpendicular line is:

\(\displaystyle{m}=-{\left(\frac{{1}}{{5}}\right)}\)

Substitute \((x_1,y_1)=(10,-2)\) so that we have: \(\displaystyle{y}-{\left(-{2}\right)}=-{\left(\frac{{1}}{{5}}\right)}{\left({x}-{10}\right)}\)

\(\displaystyle{y}+{2}=-{\left(\frac{{1}}{{5}}\right)}{x}+{2}\)

\(\displaystyle{y}=-{\left(\frac{{1}}{{5}}\right)}{x}\)