# Linear Graph Line

1. Feb 13, 2007

### thomas49th

1. The problem statement, all variables and given/known data
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°)
2. Relevant equations

y = mx + c

Last edited: Feb 13, 2007
2. Feb 13, 2007

### cristo

Staff Emeritus
What condition must the gradients of two perpendicular lines satisfy?

3. Feb 13, 2007

### thomas49th

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

4. Feb 13, 2007

### HallsofIvy

Staff Emeritus
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.

5. Feb 13, 2007

### cristo

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

6. Feb 13, 2007

### thomas49th

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

7. Feb 14, 2007

### Integral

Staff Emeritus
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.

8. Feb 14, 2007

### HallsofIvy

Staff Emeritus
Thomas49th, are you saying you cannot read our responses?

9. Feb 14, 2007

### thomas49th

aha, ingenius. It works. Thanks a load