Question

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

Answer 1

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