Perpendicular Lines: Slope, Angle & Equations

[Taturana]

A very simple and noob question, sorry for this.

Looking at http://en.wikipedia.org/wiki/Perpendicular I found that two lines are perpendicular if and only if the product of their slopes is -1.

If I have two lines described by the following equations:

y = ax + b
g = cx + d

then they're perpendicular if ac = -1 right? Okay...

What's the explanation for this? How do I conclude that they're only perpendicular if and only if the product of their slopes is -1?

Just another little question: the slope of a line is the tangent of the angle between the line and the x-axis? that's right?

Thank you

 

[tiny-tim]

HI Taturana!

How do I conclude that they're only perpendicular if and only if the product of their slopes is -1?

Just another little question: the slope of a line is the tangent of the angle between the line and the x-axis? that's right?

That's right … slope = tan, and so …

tan(90º + θ) = sin(90º + θ)/cos(90º + θ) = cosθ/(-sinθ) = -1/tanθ. ​

(or you can prove it just as easily by drawing it)