Question

Find an equation of the line through the point (1,4) and perpendicular y = 3x + 1.

Answer 1

\[4= \frac{-1}{3}*1+b\\ b= \frac{13}{3}*1\\ y=\frac{-x}{3}+ \frac{13}{3}\]

Answer 2

slope of equation y=3x+1 is 3 since ,
we have equation as y=mx+c ,where m is the slope .
when we say to lines are perpendicular it means .there slope will have product =-1
let the slope of this "required" line be n. den m*n=-1 , where m =3.
so slope of the required equation is =-1/3
then consider the point through which it is supposed to pass

Answer 3

so y-4/x-1= slope . which is n = -1/3
now simplfy this equation \[(y-4)\div (x-1) =-1/3\]