Write an equation of the line that passes through (3,2) and is perpendicular to the line y= 1/3x-3

Question

asked Jul 17, 2022 11.6k views

1 Answer

Butch · Answer 1 · 2022-07-23T01:36:06+0000

Answer:
y= -3x+11

Explanation:

Given equation:
$y=\frac13x-3$

By comparing this to intercept form
y=mx+c , where m= slope , c=y-intercept.

$m=\frac13$

Let n= slope of required line.

n* m =-1 [Product of slope of two per perpendicular line =-1 ]

$\Rightarrow\ n=(-1)/(m)\\\\\Rightarrow\ n=(-1)/(\frac13)=-3$

Equation of line passes through (a,b) and have slope m:

(y-b)=m(x-a)

Equation of required line :

$(y-2)=-3(x-3)\\\\\Rightarrow\ y-2=-3x+9\\\\\Rightarrow\ y= -3x+11$

Hence, equation of the required line: y= -3x+11