Sender: fatiha khanboubi

I was wondering if you could please explain to me how I would write the equation of line through the given points [(4,1), (6,3)] in Ax+By=C form.

I am a student in the eighth grade. Please answer as soon as possible.

Hi Fatiha,

Since (4,1) and (6,3) both lie on the line Ax + By = C they both have to satisfy the equation. Hence

4A + B = C
6A + 3B = C

Multiply both sides of the first equation by 3 so the equations become

12A + 3B = 3C
6A + 3B = C

Now if you subtract the second equation from the first you get

6A = 2C
C = 3A

At this point go back to the equation

4A + B = C

and substitute C = 3A to get

4A + B = 3A

which is

B = -A

Thus your original equation

Ax + By = C

can be written

Ax + -Ay = 3A

Finally divide both sides by A to get

x + -y = 3


Go to Math Central