# How to write an equation in standard form for a line through (-5,4); slope -3?

May 3, 2015

The most common definition of "standard form for a linear equation is
$A x + B y = C$

For a point $\left({x}_{1} , {y}_{1}\right) = \left(- 5 , 4\right)$ and a slope $m = \left(- 3\right)$
We can start from the point-slope form:
$\frac{y - {y}_{1}}{x - {x}_{1}} = m$

$\frac{y - 4}{x + 5} = - 3$

$y - 4 = - 3 x - 15$

$3 x + y = - 11$