Question

What is the slope of any line perpendicular to the line passing through `(0,2)` and `(3,15)`?

Answer 1

The slope of any line passing through the given two points is `-3/13`.

Explanation:

First find the slope of the line passing through the two given points.

`m=(y_2-y_1)/(x_2-x_1)`,

where:

`m` is the slope, and `(x_1,y_1)` and `(x_2,y_2)` are the two given points. I'm going to use point `(0,2)` as `(x_1,y_1)` and `(3,15)` as `(x_2,y_2)`. You could do the reverse and you would get the same slope.

Plug in the known values and solve for slope.

`m=(15-2)/(3-0)`

`m=13/3`

The perpendicular slope of any line is the negative reciprocal of the original slope, so that `m_1m_2=-1`.

`13/3xx-3/13=-39/39=-1`. The perpendicular slope is `-3/13`.

graph{(y+13/3x)(y-3/13x)=0 [-10, 10, -5, 5]}