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## #1 2005-12-05 01:44:51

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Perpendicular line equations.

I've completed a few of these with no problem but I am stuck on:
2x + 3y + 2 = 0,  find the equation of the perpendicular line passing through (4, 7).

2x + 3y + 2 = 0
3y = -2x - 2
y = (-2x -2)/3

perpendicular line would be :
y = 3/2 x + 4 1/3?

Aloha Nui means Goodbye.

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## #2 2005-12-05 01:58:08

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Re: Perpendicular line equations.

The perpendicular line would be:
y = 3/2 x + 1
2y = 3x + 2

What is the equation used to get to this number?

Aloha Nui means Goodbye.

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## #3 2005-12-05 03:26:06

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Perpendicular line equations.

You got the gradient right, because to find a perpendicular gradient, you divide -1 by the original gradient.

If you know a line has gradient g and passes through (x,y), then its y-intercept is y - (g*x).

For your one, it passes through (4,7) and has a gradient of 3/2, so the y-intercept is 7 - (3/2*4) = 1.

Why did the vector cross the road?
It wanted to be normal.

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## #4 2005-12-05 03:27:07

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Re: Perpendicular line equations.

Thankyou mathsy!

Aloha Nui means Goodbye.

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## #5 2005-12-05 03:30:55

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Perpendicular line equations.

Perpendicular lines slopes always share a negative inverse relationship.
Mathematically this means that the product of the two slopes always equals negative one.

m1(m2) = -1

A linear equation can always be written as mx + b = y

You were on the right track to solving this problem.

Solve for y for the original equation:  y= -2/3 x -2/3

Therefore the slope is -2/3

If the second line is perpendicular then -2/3 m2 = -1,  so m2 = 3/2 or 1.5

The second equation must then be y = 1.5x + b

Plugging in the point specified by your question:  7 = 1.5(4) + b

Solving for b and keeping the slope give you your perpendicular line equation

y = 1.5x + 1

Last edited by irspow (2005-12-05 03:32:22)

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## #6 2005-12-05 03:52:09

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Re: Perpendicular line equations.

The perpendicular line would be:
y = 3/2 x + 1
2y = 3x + 2

Thanks irspow but you're a bit late

Aloha Nui means Goodbye.

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## #7 2005-12-05 04:47:29

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Perpendicular line equations.

Sorry, my fingers are slower than my head.

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