Question

Identify the equation in point slope form for the line perpendicular to y= -1/3x-6 that passes through (-1,5).

Answer 1

A. y - 5 = 3(x + 1)

Explanation:

y = -1/3 x - 6

This line, slope = -1/3

Perpendicular lines, slope is opposite and reciprocal, so slope = 3

Equation that passes thru (-1,5)

y - 5 = 3(x + 1)

Answer 2

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

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

We have
`m_ {1} = - \frac {1} {3}`

So:

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

Then, the equation is of the form:

`y-y_ {0} = m (x-x_ {0})`

We have the point:

`(x_ {0}, y_ {0}) = (- 1,5)`

We replace:

`y-5 = 3 (x - (- 1))\\y-5 = 3 (x + 1)`

ANswer:

`y-5 = 3 (x + 1)`

Option A