Answer: [tex]x+3y=12[/tex]
Step-by-step explanation:
Slope of two lines that are perpendicular to each other is 1.
If one line is [tex]y=3x[/tex], then its slope = 3 [by comparing to the linear equation y= mx+c, here m=3]
Let n be the slope of the required line, then
[tex]n\times3=-1\\\\\rightarrow\ n=\dfrac{-1}{3}[/tex]
Equation of line with slope n and passers through (a,b) is
[tex](y-b)=n(x-a)[/tex]
Equation of line with slope n= [tex]\dfrac{-1}{3}[/tex] and passes through point ( 0,-4) :
[tex](y-(-4))=\dfrac{-1}{3}(x-0)\\\\\Rightarrow\ y+4=\dfrac{-1}{3}x\\\\\Rightarrow\ -3(y+4)=x\\\\\Rightarrow-3y-12=x\\\\\Rightarrow x+3y=12[/tex]
Hence, Required equation : [tex]x+3y=12[/tex]
