Question

How do you make a perpendicular line when you're given an existing line and its equation? What's the catch?

Answer 1

See explanation

Explanation:

The slope `m` of a line `L` that is perpendicular to another line `L'` is the negative reciprocal of the slope `m'` of `L'`

`m = -1/m'`

Now, to determine the equation of `L`, we need any point on the line so that we can determine its `y`-intercept

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Example:
Find the equation of the line `L` if it is perpendicular to the line `L'` with equation `y = 2x + 1` and `L` passes through `(1, -4)`

The slope `m'` of `L'` is 2

`=> m = -1/m' = -1/2`

Now that we have the slope, let's find the `y`-intercept.
To do this, we substitute the coordinates of a point that the line passes through. In this case, `L` passes through `(1, -4)`

`y = mx + b`

`=> -4 = -1/2(1) + b`

`=> -4 = -1/2 + b`

`=> b = -4 + 1/2`

`=> b = -7/2`

Hence, the equation of the line `L` is

`y = -1/2x - 7/2`