Question

What is the equation of the line perpendicular to `y=-1/16x` that passes through `(3,4)`?

Answer 1

Equation of desired line is `y=16x-44`

Explanation:

The equation of line `y=−(1/16)x` is in slope-intercept form `y=mx+c`, where `m` is slope and `c` is intercept on `y` axis.
Hence its slope is `−(1/16)`.

As product of slopes of two perpendicular lines is `-1`, slope of line perpendicular to `y=−(1/16)x` is `16` and slope-intercept form of the equation of line perpendicular will be `y=16x+c`.

As this line passes through (3,4), putting these as `(x, y)` in `y=16x+c`, we get `4=16*3+c` or `c=4-48=-44`.

Hence equation of desired line is `y=16x-44`