Question

Identify the equation in point slope form for the line perpendicular to y=3x+5that passes through (4,-1).

Answer 1

For this case we have that by definition, if two lines are perpendicular, then it follows that:

$m_ {1} * m_ {2} = - 1$

We have $m_ {1} = 3$

So:

$3 * m_ {2} = - 1\\m_ {2} = - \frac {1} {3}$

Thus, the equation would be:

$(y-y_ {0}) = - \frac {1} {3} (x-x_ {0})$

We have the point:

$(x_ {0}, y_ {0}) = (4, -1)$

We replace:

$(y - (- 1)) = - \frac {1} {3} (x-4)\\y + 1 = - \frac {1} {3} (x-4)$

Answer:

$y + 1 = - \frac {1} {3} (x-4)$

Option C

Answer 2

perpendicular slopes are those that are opposite signs and flipped version of original slope.