Question

Which of these lines is perpendicular to the line y = 3x + 2?

A. y = 1/3x + 3

B y= 1/3x+2

C. Y= -1/3x +4

D. y=3x + 1/2

Answer 1

(c)
`y=(-1)/(3)x+4` will be perpendicular to the line y = 3x+2

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
`=(-1)/(m)`

So the slope of the line which is perpendicular to y = 3x+2 will be
`=(-1)/(3)`

Now (a) Line is given as
`y=(1)/(3)x+3` its slope is
`(1)/(3)` so it will be not perpendicular

(b) Line is given as
`y=(1)/(3)x+2` its slope is
`(1)/(3)` so it will be not perpendicular

(c) Line is given as
`y=(-1)/(3)x+4` its slope is
`(-1)/(3)` so it will be perpendicular to the line y = 3x+2

(d) Line is given as
`y=3x+(1)/(2)` its slope is 3 so it will not perpendicular to the line y = 3x+2