Answer: [tex]y= -3x+11[/tex]
Step-by-step explanation:
Given equation: [tex]y=\dfrac13x-3[/tex]
By comparing this to intercept form [tex]y=mx+c[/tex] , where m= slope , c=y-intercept.
[tex]m=\dfrac13[/tex]
Let n= slope of required line.
[tex]n\times m =-1[/tex][Product of slope of two per perpendicular line =-1 ]
[tex]\Rightarrow\ n=\dfrac{-1}{m}\\\\\Rightarrow\ n=\dfrac{-1}{\dfrac13}=-3[/tex]
Equation of line passes through (a,b) and have slope m:
[tex](y-b)=m(x-a)[/tex]
Equation of required line :
[tex](y-2)=-3(x-3)\\\\\Rightarrow\ y-2=-3x+9\\\\\Rightarrow\ y= -3x+11[/tex]
Hence, equation of the required line: y= -3x+11
