Question

How do you write an equation of a line passing through (0, 4), perpendicular to `y = x`?

Answer 1

`y = -x+4`

Explanation:

We have been given one point `(0,4)` and (indirectly) the slope.

It lines are perpendicular, then one slope is the negative reciprocal of the other.

In `y =x`, it is actually `y = +1x" "` so the slope, `m=1`
The slope perpendicular to this will be `m=-1`

The point we have been given is a specific point:

It is the `y`-intercept, `c=4`, so we have everything we need to write the equation of the line in the form `y = mc+c`

`y = -x+4`