Co-ordinate geometry help

**Chris85** · October 1st 2007, 06:45 AM

Hi, what is the best way to find the equation of a straight line when given to points on the line. ie (x1,y1) and (x2,y2)

I have been finding the gradient m=y2-y1/x2-x1 and then putting into the formula y-y1 =m(x-x1) but i am doing something wrong as i keep getting different answers to my textbook. Could somebody please solve one for me so i can see how it's done?

Heres one in my book Find the equation of the line AB when A(-2,4) B(5,3)

Thanks, Chris.

**Krizalid** · October 1st 2007, 07:19 AM

Find $m$

$m=\frac{3-4}{5+2}=-\frac17$

Now select one point and apply the point-slope formula.

**red_dog** · October 1st 2007, 07:28 AM

The equation of a line passing through two points $M_1(x_1,y_1), \ M_2(x_2,y_2)$ is

$\displaystyle\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}$

or $\displaystyle\begin{vmatrix}x & y & 1\\x_1 & y_1 & 1\\x_2 & y_2 & 1\end{vmatrix}=0$

**Chris85** · October 1st 2007, 07:39 AM

Hi thanks. Yes i know the formula, it's just i am having trouble using it

i am going wrong somewhere with it.

**topsquark** · October 1st 2007, 08:02 AM

Originally Posted by Chris85

Hi thanks. Yes i know the formula, it's just i am having trouble using it

i am going wrong somewhere with it.

Why don't you post your solution and we'll take a look at it.

-Dan

**Chris85** · October 1st 2007, 09:37 AM

OK

A=(-2,4) B=(5,3)

M= y2-y1/x2-x1 = 3-4/5-(-2) = -1/7

y-y1/y2-y1 = x-x1/x2-x1

therefore y-4/3-4 = x-(-2)/5-(-2)

Am i right so far if so what do i do next?? apologies if it's hard to understand im new and still trying to do the latex

**earboth** · October 1st 2007, 10:03 AM

Originally Posted by Chris85

OK

A=(-2,4) B=(5,3)

M= y2-y1/x2-x1 = 3-4/5-(-2) = -1/7

y-y1/y2-y1 = x-x1/x2-x1

therefore y-4/3-4 = x-(-2)/5-(-2)

Am i right so far if so what do i do next?? apologies if it's hard to understand im new and still trying to do the latex

Hello,

you calculated the slope of the line correctly.

Now you plug in the coordinates of one point into the equation of the line:

point-slope-formula, see Krizalid's post.
$\frac{y-y_1}{x-x_1} = m~\implies~\frac{y-3}{x-5}=-\frac17$ Solve for y:

$y-3 = -\frac17 \cdot(x-5)$ expand the bracket and solve for y:

$y = -\frac17 \cdot x + \frac{26}7$

**Chris85** · October 1st 2007, 12:16 PM

ok, the answer in my textbook is x+7y-26=0??

**earboth** · October 3rd 2007, 09:37 PM

Originally Posted by Chris85

ok, the answer in my textbook is x+7y-26=0??

Hi,

take the result I gave you, multiply both sides by 7 and collect all terms on the LHS - then you'll get the answer which is in your book.

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