1. ## Co-ordinate geometry help

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.

2. Find $\displaystyle m$

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

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

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

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

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

4. Hi thanks. Yes i know the formula, it's just i am having trouble using it i am going wrong somewhere with it.

5. 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

6. 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

7. 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.
$\displaystyle \frac{y-y_1}{x-x_1} = m~\implies~\frac{y-3}{x-5}=-\frac17$ Solve for y:

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

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

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

9. 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.