Question

How do you write an equation that contains points (5, -3) and is perpendicular to y=5x?

Answer 1

`y = -1/5 x - 2`

Explanation:

We know that this point goes through a point, but in order to define a line we need either two points or a point and a slope.

We can get that slope from the above equation. We know that the new line will have slope perpendicular to five. Perpendicularity means negative inverse, i.e. `m = - 1 / 5`.

From that, we know point-slope form:
`y-y_1 = m(x-x_1) implies y + 3 = -1/5(x - 5)`
`y = -1/5 x - 2`