# How do you write an equation in standard form for a line passing through (–2, 8) with a slope of 2?

May 1, 2015

Standard form for a line is $a x + b y = c$

Start in point slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $\left({x}_{1} , {y}_{1}\right)$ is a point on the line and $m$ is the slope.

$y - 8 = 2 \left(x - \left(- 2\right)\right)$

Now simplify and remove the parentheses (by distributing the $2$):

$y - 8 = 2 \left(x + 2\right)$

$y - 8 = 2 x + 4$

To get slope-intercept form, we would get the $y$ alone by adding $8$.

But we've been asked for standard from, so we need to get the $x$ and $y$ together and everything else on the other side:

Subtract $2 x$ (or add $- 2 x$ -- it's the same) and add $8$ to get:

$y - 2 x = 4 + 8 = 10$

We need the $x$ term first, (remember the $- 2$ is stuck to the $x$) so:

$- 2 x + y = 12$

If you don't like the $-$ sign in front of the $x$, you can multiply both sides by $- 1$ (although this will put a $-$ sign in front of the $12$)

$- 1 \left(- 2 x + y\right) = \left(- 1\right) \left(12\right)$

$2 x - y = - 12$

May 1, 2015

The most commonly accepted version of "standard form" for a linear equation in two unknowns is:
$A x + B y = C$ for some constants $A , B , C$

The equation of a line through $\left(- 2 , 8\right)$ with a slope of $2$ is
$\frac{y - 8}{x - \left(- 2\right)} = 2$

$y - 8 = 2 x + 4$

$- 2 x + y = 12$