Why is y = -1/3·x - 4 perpendicular to y = 3x + 4?

[thomas49th]

Homework Statement

The line l has equation y = 3x + 4
Cans someone xplain how $$y = -\frac{1}{3}x-4$$ is perpendicular to line l(bisects l at 90°)

Homework Equations

y = mx + c

 

[cristo]

What condition must the gradients of two perpendicular lines satisfy?

 

[thomas49th]

negtive gradient.

y = mx + c where m is a negitive number?

 

[HallsofIvy]

No, remember that the slope of a line is the tangent of the angle the line makes with the x-axis. If two lines are y= m₁x+ b and y= m₂x+ c, then the two lines are parallel if and only if m₁= m₂ and parallel if and only if (m₁)(m₂)= -1.

Those can both be derived from properties of the tangent function.

 

[cristo]

and parallel if and only if (m₁)(m₂)= -1.

Just correcting a typo: you mean perpendicular if and only if (m₁)(m₂)= -1.

 

[thomas49th]

perpendicular if and only if (m1)(m2)= -1.

cant it be

perpendicular if and only if (m1)(m2)= -0.5? Or any other number there? Was that just an example? If not what is so special about -1?

(m1)(m2)= -1
so 3 * -1/3 = -1

cheerz, Big help

 

[Integral]

Graph a set of perpendicular intersecting lines.

Now using the graphs, compute the slopes, can you now see why the relationship is $m_1 m_2 = -1$

You may need to look at several sets of lines to see the relationships.

 

[HallsofIvy]

Thomas49th, are you saying you cannot read our responses?

 

[thomas49th]

aha, ingenius. It works. Thanks a load