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

 The correct option is

(D)

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) :

We know that

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

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

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

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

Thus, the required equation of the line is

Option (D) is CORRECT.

step-by-step explanation: