# Equations Of Straight Lines?

• Apr 9th 2009, 09:10 AM
Sailee316
Equations Of Straight Lines?
Hi. I have this question im my assignment

Find the equation of the straight lines that pass through the points:
(i) (2, -1) and (-4, -19)
(ii) (0, -1/3) and (5, 2/3)
Where do these two lines meet?

I dont know how to do it. Do I actually have to draw the graph? Or is there some way of finding the equations and intercept using a formula or something?

Thanks
• Apr 9th 2009, 09:31 AM
molimoli
find the gradient first using

m= y-y1 / x-x1 (minus y values from each other the minus x values )

-1+19 / 2+4 therefore m= 18/6 so m = 3 which is your gradient

then choose one of your 2 points so for eg (2,-1)

then use y= mx+c

-1= 3 (2) + c
-1 = 6+c
c = -7

the equation is y= 3x-7

you can solve the part 2 the same way. to find where the lines intersect, make them equal to each other then find x and y.
• Apr 9th 2009, 02:44 PM
stapel
Quote:

Originally Posted by Sailee316
I dont know how to do it. Do I actually have to draw the graph?

No, you don't have to graph the lines. And graphing probably wouldn't help you answer the questions. (Blush)

Quote:

Originally Posted by Sailee316
...is there some way of finding the equations and intercept using a formula or something?

Yes, there is a way, including "a formula", which they were supposed to have mentioned before now! (Surprised)

To find the slope of the line through a pair of points, plug those points into the slope formula.

To find the equation of the line through that pair of points, pick one of the points (it doesn't matter which), and plug it, along with the slope you just found, into the point-slope form of the line equation.

Depending on your book, you may or may not need to "simplify" or rearrange the equation from there. (Wink)