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

Sep 13, 2015

8x+9y=39

#### Explanation:

Let's start with equation of the line in the form $y = k x + n$. 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: $- 1 = 6 k + n$
for B: $7 = - 3 k + n$
Now, we have to solve this system of equations, the easiest way is to subtract them. We get:
$- 1 - 7 = 6 k + n - \left(- 3 k + n\right)$
$- 8 = 6 k + n + 3 k - n$
$- 8 = 9 k$
$k = - \frac{8}{9}$
$- 1 = 6 \left(- \frac{8}{9}\right) + n$
$n = - 1 + \frac{48}{9}$
$n = \frac{39}{9}$
So, finding $k , n$ we can form $y = k x + n$
$y = - \frac{8}{9} x + \frac{39}{9}$
Multiplying whole equation with 9:
$9 y = - 8 x + 39$
we finally get:
$8 x + 9 y = 39$