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)?

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) :

$y=-\dfrac{1}{3}x+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

$m=-\dfrac{1}{3}.$

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

$m\times m'=-1\\\\\Rightarrow -\dfrac{1}{3}\times m'=-1\\\\\Rightarrow m'=3.$

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.