Answer:
y = [tex]\frac{-1}{3}[/tex]x + c.
Step-by-step explanation:
We are given with the line y = 3x + 1 .
Now , we have to find the lines perpendicular to it .
Thus , we have to consider its slope for calculating the slope of required perpendicular lines.
Now, slope of the given line is [tex]m_{1}[/tex] = 3.
Let the slope of the perpendicular lines be [tex]m_{2}[/tex] .
Since the two lines of slope [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are perpendicular [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1
Thus , [tex]m_{2}[/tex] = [tex]\frac{-1}{3}[/tex].
So, all lines having the slope [tex]\frac{-1}{3}[/tex] are perpendicular to the given line , these lines may be represented by
y = [tex]\frac{-1}{3}[/tex]x + c.
