Question

What is the equation of the line perpendicular to `y=-5/7x` that passes through `(1,-4)`?

Answer 1

`5y =7x -27`

Explanation:

If a line has slope `m` then the line perpendicular to it has slope `-1/m`.
Therefore the slope of the line perpendicular to `y =-5/7*x` has slope `7/5`.
Using the general equation of a straight line `y=mx+c` and the coordinates of the given point, we have
`-4 = (7/5)(1) + c`
`-4 -7/5 = c`
`c = -27/5`
The equation of the line is therefore `y = 7/5*x - 27/5` or

`5y =7x -27`