Answer:
(c) [tex]y=\frac{-1}{3}x+4[/tex] will be perpendicular to the line y = 3x+2
Step-by-step explanation:
We have given the the equation of line as y = 3x+2
We know the equation of line as y = mx+c , here m is slope and c is intercept
On comparing with standard equation of line m = 3
We know that slope of perpendicular line is [tex]=\frac{-1}{m}[/tex]
So the slope of the line which is perpendicular to y = 3x+2 will be [tex]=\frac{-1}{3}[/tex]
Now (a) Line is given as [tex]y=\frac{1}{3}x+3[/tex] its slope is [tex]\frac{1}{3}[/tex] so it will be not perpendicular
(b) Line is given as [tex]y=\frac{1}{3}x+2[/tex] its slope is [tex]\frac{1}{3}[/tex] so it will be not perpendicular
(c) Line is given as [tex]y=\frac{-1}{3}x+4[/tex] its slope is [tex]\frac{-1}{3}[/tex] so it will be perpendicular to the line y = 3x+2
(d) Line is given as [tex]y=3x+\frac{1}{2}[/tex] its slope is 3 so it will not perpendicular to the line y = 3x+2
