Question

How do you write an equation of a line passing through (6, 4), perpendicular to `y=3x - 2`?

Answer 1

`x+3y-18=0`

Explanation:

Slope intercept form of equation of a line is `y=mx+c`, where `m` is its slope and `c` is its intercept on `y`-axis. As such slope of `y=3x-2` is `3`.

As product of slopes of two lines perpendicular to each other is `-1`, hence slope of line perpendicular to `y=3x-2` is `-1/3`.

Equation of a line passing through `(x_1,y_1)` and having a slope of `m` is `(y-y_1)=m(x-x_1)`. Hence equation of line passing through `(6,4)` and slope of `-1/3` is

`(y-4)=-1/3(x-6)` or

`3y-12=-x+6` or

`x+3y-12-6=0` i.e.

`x+3y-18=0`