# 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