Question

How do you write the equation of the line in the form AX+BY=C if (9, -8) and (0, 3)?

Answer 1

`11/9 x +y=3`

Explanation:

Okay, the line passes through these two points, and the equation of a line is usually in the form `y=ax+b`.

Then the point (9, -8) is because:
`-8=a*9+b`
and the point (0, 3) is because:
`3=a*0+b`

We just need to solve for a and b to find the equation of the line.
From the second equation we readily see that `b=3`.

Now substitute this `b` into the equation of the first point:
`-8=a*9+3`
Rearranging, we have:
`9a=-11`
so `a=-11/9`

So the equation of the line is: `y=-11/9 x +3`
Rearranging, we get:
`11/9 x +y=3`
which is in the desired form `Ax+By=C`
where `A=11/9`, `B=1`, and `C=3`