Question

How do you find the equation of a line that Contains point (5, -3) and is perpendicular to y=5x?

Answer 1

`y=-1/5x -2`

Explanation:

For finding an equation of a perpendicular line, we start with finding the slope of the given line. Slope of the perpendicular line is negative reciprocal of the given slope. For example, if the slope is `m` then the slope of the perpendicular would be `-1/m`

Equation of the form `y=mx+b` has the slope as `m`

Using this knowledge, we can see that the slope of the line `y=5x` is `5`

The slope of the perpendicular line is `-1/5`

We can say our line would be

`y=-1/5x + b`

We need to find `b` to find the equation. This is where the point`(5,-3)` is used.

Let us substitute the value `x=5` and `y=-3` in the equation `y=-1/5x+b`

We get,
`-3=-1/5(5)+b`
`-3=-1+b`
Add `1` to both the sides.

`-3+1=b`

`-2=b`

Our equation becomes `y=-1/5x -2`