Negative Reciprocals of Slopes and Perpendicular Lines

[baily106]

Hello,

There is a discussion about negative reciprocals of slopes and lines that are perpendicular. How do you know based on formula as opposed to looking at a graph that two lines are perpendicular or that their slopes are negative reciprocals of each other?

Thanks,
Anisha

[tommywallach]

Hey Anisha,

Negative reciprocals can actually be read MOST easily from an equation (you can't just look at a picture, because lines aren't always drawn to scale, so you have to know from an equation, or from the question literally telling you "These lines are perpendicular"):

y = 2x + 12
y = -1/2x - 4

These two lines are perpendicular, because their slopes are negative reciprocals of each other.

-t

P.S. I noticed you put up a lot of posts/questions in the forum. I'm happy to answer them. However, I will ask three things: 1) Please post the question itself in any thread (so that other people can weigh in without having to find the book). 2) Please discuss where the question went wrong or confused you, as opposed to just asking for a bottom to top explanation I'd prefer not to simply solve questions, but answer questions you have about questions. 3) Title the thread with the book name, page number, and question number, so the thread is useful to other folks.

Thanks so so much!

-t

[baily106]

Thanks T.

I see how the 2x becomes a -1/2X, but how does the 12 become a negative 4? Also, is it -1/2x and -4 because it is a positive 2 and a positive 12? In other words, does the sign always change?

I will repost the other questions.

Anisha

[tommywallach]

Hey Baily,

The y-intercept has nothing to do with slope. I just chose those numbers arbitrarily. Slope and y-intercept have no bearing on each other. If the slopes are negative reciprocals, then the two lines meet perpendicularly.

-t

P.S. I'll change them now, but in the future, please give each posting TITLE the name of the question.