# Linear Graph Line

## 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

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

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

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

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
Staff Emeritus
Gold Member
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
Homework Helper
Thomas49th, are you saying you cannot read our responses?

aha, ingenius. It works. Thanks a load