Question

How do you write an equation of a line perpendicular to `y=1/4x+2` and passes through (0,0)?

Answer 1

`color(green)(y=-4x)`

Explanation:

The given equation : `y=color(red)(1/4)x+color(blue)2`
is in slope-intercept form with slope `color(red)(1/4)`

If a line has slope `color(red)m` then all lines perpendicular to it have slopes of `color(magenta)(-1/m)`

Therefore any line perpendicular to the given line must have a slope of `color(magenta)(-4)`
and since the requested line is to pass through `(0,0)` (which implies a y-intercept of `color(blue)(0)`
in slope-intercept form this line must have an equation:
`color(white)("XXX")y=color(magenta)(-4)x+color(blue)0`
or just
`color(white)("XXX")y=color(magenta)(-4)x`