Question

Question #b8968

Answer 1

`"slope "=-1/m`

Explanation:

`"given a line with slope m then the slope of a line"`
`"perpendicular to it is"`

`•color(white)(x)m_(color(red)"perpendicular")=-1/m`

Answer 2

The slope of the lines must be negative reciprocals of each other.

Explanation:

Basically, if you have the slope of a straight line, and you need to find the slope of a line perpendicular to it, you need to flip the number, and make it negative. For example, if you have a line `y=1/2x+2`, then the equation of a line perpendicular to it will be: `y=-2x+c`.

All I've done is flip the coefficient of x(the slope) and add the negative sign to it. (also, I've written the y-intercept as `c` because unless you have a point that the perpendicular line passes through, you don't know where it crosses the y-axis)

Here's a link that explains the concept and has some examples: http://www.purplemath.com/modules/slope3.htm

(here's the proof for it if you're interested: https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/proof-that-perpendicular-lines-have-negative-reciprocal-slope -don't let this confuse you though, all you have to do is flip the number and add the negative sign!)