# How do you write the equation of the line in the form AX+BY=C if m = 1, P (2, -4)?

Oct 6, 2015

$1 x + \left(- 1\right) y = 6$

#### Explanation:

Given a slope of $m = 1$ and a point $\left(\hat{x} , \hat{y}\right) = \left(2 , - 4\right)$
we can substitute these values into the general point-slope form:
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$
to get
$\textcolor{w h i t e}{\text{XXX}} \left(y + 4\right) = 1 \left(x - 2\right)$
This can be re-arranged fairly easily to form:
$\textcolor{w h i t e}{\text{XXX}} 1 x + \left(- 1\right) y = 6$
which is the requested form