Answer to Question #201825 in Geometry for tynasia

Question

miguel finds the equation of a line that is perpendicular to y=ax+b

. If he multiplies the slopes of the two lines, what is the product?

Answer 1

Slope of a line y=mx+c is m

Equation of a perpendicular line to the line ax+by+c =0

is bx-ay+k=0

Given the equation of a line is:-

y=ax+b

$\therefore$ Slope of this line =a

Now,

y=ax +b

$\implies$ ax-y+b=0

$\therefore$ General equation of a perpendicular line to ax-y+b=0 is ,

-x-ay+k=0

$\implies$ -ay=x-k

$\implies y=-\frac{1}{a}x+\frac{k}{a}$

$\therefore Slope of the perpendicular line =-\frac{1}{a}$

Hence, the product of the slope =$a \cdot( \frac{-1}{a})$

=-1