For this case we have that by definition, if two lines are perpendicular, then it follows that:
[tex]m_ {1} * m_ {2} = - 1[/tex]
We have [tex]m_ {1} = 3[/tex]
So:
[tex]3 * m_ {2} = - 1\\m_ {2} = - \frac {1} {3}[/tex]
Thus, the equation would be:
[tex](y-y_ {0}) = - \frac {1} {3} (x-x_ {0})[/tex]
We have the point:
[tex](x_ {0}, y_ {0}) = (4, -1)[/tex]
We replace:
[tex](y - (- 1)) = - \frac {1} {3} (x-4)\\y + 1 = - \frac {1} {3} (x-4)[/tex]
Answer:
[tex]y + 1 = - \frac {1} {3} (x-4)[/tex]
Option C
