I need point/slope formula help!

 Mathematics Tutor: None Selected Time limit: 1 Day

I am preparing for the NY State Geometry Regent, and I answered a multiple-choice point/slope question. The question reads: What is an equation of the line that passes through (-9,12) and is perpendicular to the line whose equation is y = 1/3x + 6?

The correct answer was: y = -3x - 15.

I went over the math once again after seeing the correct answer. I still got y = 1/3x + 15. I don't see how the answer is y = -3x - 15. Can someone please explain the problem to me?

Jun 18th, 2015

The given line is y = 1/3 x + 6
let the slope of the line be m1, comparing with the standard form y=mx+c
we get, m1= 1/3

let the slope of the required line be m2
since both the lines are perpendicular to each other, m1*m2 =-1
so, 1/3*m2 = -1
m2 =-3

so, the required equation will be y= -3x + c

since this line passes through (-9,12)
we get 12 = -3*-9 + c
12 = 27 +c
c = 12-27 = -15

so, the required equation is y = -3x -15

Please let me know incase you have any doubts :)

Please appreciate my help and select my answer as the best! Thanks :) Please appreciate my help and select my answer as the best! Thanks :)
Jun 18th, 2015

You said: Since both of the lines are perpendicular to each other, m1 * m2 = -1.  Where did this -1 come from?

Jun 18th, 2015

this is the basic formula.

If lines are parallel then m1 = m2
if lines are perpendicular then m1 * m2 = -1

Please check your text book, it would be mentioned somewhere. Let me know if you still have any doubt.

Jun 18th, 2015

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Jun 18th, 2015
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Jun 18th, 2015
Dec 6th, 2016
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