Write the general form of a line through the point T of intersection of the two lines 2x - 3y + 6 = 0 and x + 3y - 15 = 0

Please help I have no idea how to do this.

Thanking You

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- Jun 27th 2010, 03:43 AMJoelWrite the general form of the line...
Write the general form of a line through the point T of intersection of the two lines 2x - 3y + 6 = 0 and x + 3y - 15 = 0

Please help I have no idea how to do this.

Thanking You - Jun 27th 2010, 03:59 AMZaph
Set the two equations equal to eachother, and solve for y

- Jun 27th 2010, 04:07 AMJoel
1. 2x - 3y + 6 = 0

2. x + 3y - 15 = 0

rearrange 2.

x = 15 - 3y

back into 1

2(15 - 3y) - 3y + 6 = 0

30 - 6y - 3y + 6 = 0

36 = 9y

y = 4

therefore x = 3

Now what do i do next ???

y - y1 = m(x - x1)

y - 4 = m(x - 3)

y = mx - 3m - 4 ??? - Jun 27th 2010, 04:17 AMZaph
Yup that's the intersection.

- Jun 27th 2010, 04:42 AMJoel
is the general form y = mx - 3m - 4 ???

- Jun 27th 2010, 05:15 AMZaph
Well if i have understood your question right, it would be y=ax+b, where (x,y)=T=(3,4) so the general form would be 4=a*3+b, where a is the slope, and b is the intersection with the y-axis?

- Jun 27th 2010, 05:51 AMJoel
Am I correct to assume the case general form is ax + by + c = 0

then

Y = MX + B in this case is y = mx - 3m - 4

-MX + Y - B = 0

sooo is it....

-mx + y + 3m + 4 = 0 ??? - Jun 27th 2010, 06:13 AMmr fantastic
The answer I have highlighted answers the question. So this answer is fine. Stop now - no need to worry any further.

I never could see the point in further re-working of a perfectly good answer. Every further bit of unnecessary additional working creates the opportunity for making a mistake. If your**final**answer is wrong, you will lose the answer mark, regardles of whether or not an earlier answer was correct. And as it happens, your last linewrong. Which only goes to prove my point.**is**