Writing Equations of Perpendicular Lines

a

Parallel lines have the same slopes which means that they have the same slope. The slope is determine by the coefficient in front of the $x$ -term. $y = a x + 2 y = 3 x - 8$ Thus, $a = 3$ will make the lines parallel.

b

If the lines are perpendicular, the product of their slopes will be equal to

- 1 .

Thus, we can find that value of

a

by solving

m_{1} \cdot m_{2} = - 1

where

m_{1}

is

a

and

m_{2}

is the slope of the line

y = 3 x - 8 .

m_{1} \cdot m_{2} = - 1

SubstituteII

m_{1} = a

,

m_{2} = 3

a \cdot 3 = - 1

DivEqn

LHS / 3 = RHS / 3

a = \frac{- 1}{3}

MoveNegNumToFracPut minus sign in front of fraction

a = - \frac{1}{3}

The slope $a$ must be equal to $- \frac{1}{3}$ if the lines are perpendicular.

Writing Equations of Perpendicular Lines 1.8 - Solution