# Write the equation of a line perpendicular to y=1/4x-5 that passes through the point (-1,2)

Question
Linear equations and graphs
Write the equation of a line perpendicular to $$\displaystyle{y}=\frac{{1}}{{4}}{x}-{5}$$ that passes through the point (-1,2)

2020-12-28
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

### Relevant Questions

A line passes through the point (2, 1) and has a slope of $$\frac{-3}{5}$$.
What is an equation of the line?
A.$$y-1=\frac{-3}{5}(x-2)$$
B.$$y-1=\frac{-5}{3}(x-2)$$
C.$$y-2=\frac{-3}{5}(x-1)$$
D.$$y-2=\frac{-5}{3}(x-1)$$
Write an equation of the line that passes through the points.
(2, 5), (0, 5)
Give the equation of the line perpendicular to the line described and satisfying the given conditions. $$\displaystyle{y}=-{\left(\frac{{4}}{{3}}\right)}{x}+{5}$$ with y-intercept (0, -8)
Find the value of r so the line that passes through each pair of points has the given slope. (r, -5), (3, 13), m = 8
A graph of a linear equation passes through ( -2,0) & (0,-6) is the 3x-y=6, both ordered pairs solutions for the equation