# How do you write the equation of the line in the form AX+BY=C if (-6, 6) and (3, -4)?

Apr 22, 2018

$- \frac{2}{3} = \frac{10}{9} x + y$

#### Explanation:

We use the slope-intercept form:

$m \left(x - {x}_{1}\right) = y - {y}_{1}$

We find the slope using this formula:

$m = \frac{{x}_{2} - {x}_{1}}{{y}_{2} - {y}_{1}}$

$\implies m = \frac{- 4 - 6}{3 - \left(- 6\right)}$

$\implies m = - \frac{10}{9}$

We let ${x}_{1} = - 6$ and ${y}_{1} = 6$

$\implies - \frac{10}{9} \left(x - \left(- 6\right)\right) = y - 6$

$\implies - \frac{10}{9} \left(x + 6\right) = y - 6$

$\implies - \frac{10}{9} x - \frac{20}{3} = y - 6$

$\implies - \frac{10}{9} x - \frac{2}{3} = y$

$\implies - \frac{2}{3} = y + \frac{10}{9} x$

$\implies - \frac{2}{3} = \frac{10}{9} x + y$

We see that $A = \frac{10}{9}$, $B = 1$, and $C = - \frac{2}{3}$