Question

Which of the following is the equation of a line perpendicular to the line y=-1/3x+1, passing through the point (2,7)?

A. -3x-y=1
B. 3x-y=1
C. -3x+y=-1
D. 3x-y=-1

Answer 1

The answer is y=3x+1. So the correct choice is letter choice D.

Answer 2

Answer: The correct option is

(D)
`3x-y=-1`

Step-by-step explanation: We are given to select the equation of a line that is perpendicular to the following line and passing through the point (2, 7) :

`y=-(1)/(3)x+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the equation of a line in slope-intercept form is given by

`y=mx+c,` where m is the slope and c is the y-intercept of the line.

Comparing the above slope-intercept form with equation (i), we get

the slope of the line (i) is

`m=-(1)/(3).`

Let m' be the slope of the required line. Since the product of the slopes of two perpendicular lines is -1, so we must have

`m* m'=-1\\\\\Rightarrow -(1)/(3)* m'=-1\\\\\Rightarrow m'=3.`

Since the line passes through the point (2, 7), so its equation will be

`y-7=m'(x-2)\\\\\Rightarrow y-7=3(x-2)\\\\\Rightarrow y=3x-6+7\\\\\Rightarrow 3x-y=-1`

Thus, the required equation of the line is
`3x-y=-1`

Option (D) is CORRECT.