Question

What is the equation of the line perpendicular to `y=-5/11x` that passes through `(1,-3)`?

Answer 1

`11x-5y=26`

Explanation:

`y=-5/11x` has a slope of `(-5/11)`

For any line with a slope of `m` all lines perpendicular to it have a slope of `(-1/m)`

Therefore any line perpendicular to `y=-5/11x` has a slope of `11/5`.

If such a line passes through the point `(1,-3)` then we can write its equation in the slope-point form (`y-haty=m(x-hatx)`)

So our required line can be written as:
`color(white)("XXX")y-(-3) = 11/5(x-1)`

While this is a valid answer to the given question, we would normally simplify it and convert it into standard form:

`color(white)("XXX")5(y+3)=11(x-1)`

`color(white)("XXX")5y+15 = 11x -11`

`color(white)("XXX")26 = 11x -5y`

`color(white)("XXX")11x -5y = 26`