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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

**Exercises on Writing Linear Equations Given Two Points**

*Write an equation of the line that passes through the given two points.*

**1. (1,2) , (21,-58)2. (5,1) , (11,-23)3. (1,5) , (7,8)4. (3,8) , (37,-60)5. (29,48) , (55,9)6. (8,-7) , (133,668)7. (-6,-6) , (78,183)8. (-19,10) , (47,-210)9. (0,5) , (45, -220)10. (22,-41) , (58,-23)11. (-39,-27) , (41,357)12. (-2,-8) , (42,-63)13. (-10,-26) , (40,-36)14. (-5,-24) , (19,-136)15. (-5,4) , (35,64)16. (3,-1) , (31,-85)17. (37,49) , (47,24)18. (-11,-6) , (27,-215)**

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**Prakash Panneer****Member**- Registered: 2006-06-01
- Posts: 110

This is the formula for finding the equation of line when the two points ( x1, y1) and (x2, y2) are given,

(y - y1)(x2 - x1) = (x - x1) (y2 - y1).

Using this formula, we can find an equation of a line for the given points.

Letter, number, arts and science

of living kinds, both are the eyes.

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**littlelittle****Member**- Registered: 2007-01-24
- Posts: 10

Hi

Stuck again..

An equation is y = mx + b where m is the slope ie. y1-y2/x1-x2.

How do i calculate 'b' without drawing n connecting the points?

Prakash - how do i put your formula to work? Can you do 1 prob for me please?

Thanks

S

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

Well, let's take for example, the coordinates (1,4) (-3, 5).

The coordinates are of the form (x1, y1) (x2, y2), so we can substitute them into the formula:

(y - y1)(x2 - x1) = (x - x1) (y2 - y1)

(y - 4)(-3 - 1) = (x - 1)(5 - 4)

(y - 4)(-4) = (x - 1)(1)

Using the distributive law:

-4(y - 4) = 1(x-1)

-4y + 16 = x - 1

-4y = x - 17

∴ y = -1/4x + 17/4

(I personally don't use this method [although it would probably benefit me if I did], instead, I find the gradient (y2-y1)/(x2-x1), then substitute the coordinate points in to solve for c)

*Last edited by Toast (2007-01-25 00:08:21)*

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**littlelittle****Member**- Registered: 2007-01-24
- Posts: 10

Thanks Toast.

Its now clear to me.

Thanks again

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**smithlanger****Member**- Registered: 2010-09-29
- Posts: 1

sounds good to me

smith

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,265

Hi smith;

Welcome to the forum. There are actually easier ways to do that.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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