Question

How do you write the equation of the line in the form AX+BY=C if A(6, -1) and B (-3, 7)?

Answer 1

8x+9y=39

Explanation:

Let's start with equation of the line in the form `y=kx+n`. We have two points with `x` and `y` coordinates, e.g. for point A: `x=6, y=-1`, for point B: `x=-3, y-7`. Next, we insert those coordinates in the equation mentioned above and get 2 equation:
for A: `-1=6k+n`
for B: `7=-3k+n`
Now, we have to solve this system of equations, the easiest way is to subtract them. We get:
`-1-7=6k+n-(-3k+n)`
`-8=6k+n+3k-n`
`-8=9k`
`k=-8/9`
`-1=6(-8/9)+n`
`n=-1+48/9`
`n=39/9`
So, finding `k, n` we can form `y=kx+n`
`y=-8/9x+39/9`
Multiplying whole equation with 9:
`9y=-8x+39`
we finally get:
`8x+9y=39`