# Thread: Write the general form of the line...

1. ## Write 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

Thanking You

2. Set the two equations equal to eachother, and solve for y

3. 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 ???

4. Yup that's the intersection.

5. is the general form y = mx - 3m - 4 ???

6. 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?

7. 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 ???

8. Originally Posted by Joel
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 ???
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 line is wrong. Which only goes to prove my point.