Question

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

Answer 1

`y=x-6`

Explanation:

We can find the gradient of a perpendicular line by the negative inverse of the first line's gradient. So, as the gradient of the line you are given is -1, the gradient (m) of a line perpendicular to it would be `-1/(-1)` which is `-(-1) = 1`

To find the equation of any line, we can use the formula
`y-y_1 = m(x-x_1)` where `y_1` and `x_1` are coordinates the line passes through.
Let's sub in our values - `m=1`, `x_1 = 5` (from the coordinates) and `y_1 = -1`
So, `y-(-1)=1(x-5)`
`y+1 = x-5`
`y=x-6`

Hope this helped; let me know if I can do anything else:)