Use the point-slope form of a line:

y−y1=m(x−x1) where mm is the slope and (x1,y1) is a point on the line.

Two lines are perpendicular if their slopes are negative reciprocals. The given line $ \(\displaystyle{y}={\frac{{{1}}}{{{4}}}}{x}-{5}\$\) has a slope of −4. So, the slope of the perpendicular line is:

m=−4

Substitute (x1,y1)=(−1,2) so that we have:

y−2=−4(x−(−1))

y−2=−4x−4

y=−4x−2

y−y1=m(x−x1) where mm is the slope and (x1,y1) is a point on the line.

Two lines are perpendicular if their slopes are negative reciprocals. The given line $ \(\displaystyle{y}={\frac{{{1}}}{{{4}}}}{x}-{5}\$\) has a slope of −4. So, the slope of the perpendicular line is:

m=−4

Substitute (x1,y1)=(−1,2) so that we have:

y−2=−4(x−(−1))

y−2=−4x−4

y=−4x−2