Question

Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, −1).

Answer 1

First find the gradient of the line: 3x + y = 7
y= -3x + 7
Gradient is given by the coefficient of x which is -3 in this case.
The gradient perpendicular to -3 is 1/3
Given the points (6,-1) and gradient,m =1/3

Substitute it into the equation for a line y=mx+c
-1 = 1/3(6) +c
c= -3

Eqn of line, y= 1/3 x-3