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Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Writing Linear Equations Given Two Points

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

Re: Writing Linear Equations Given Two Points

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.

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Letter, number, arts and science
of living kinds, both are the eyes.

littlelittle

Member

Registered: 2007-01-24

Posts: 10

Re: Writing Linear Equations Given Two Points

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

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Writing Linear Equations Given Two Points

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)

littlelittle

Member

Registered: 2007-01-24

Posts: 10

Re: Writing Linear Equations Given Two Points

Thanks Toast.

Its now clear to me.

Thanks again

smithlanger

Member

Registered: 2010-09-29

Posts: 1

Re: Writing Linear Equations Given Two Points

sounds good to me

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smith

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Writing Linear Equations Given Two Points

Hi smith;

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.