# How do you write y = 1/2x – 3 in standard form?

Mar 22, 2018

$x - 2 y = 6$

#### Explanation:

$\text{the equation of a line in "color(blue)"standard form }$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

$\text{multiply all terms in the equation by 2}$

$\Rightarrow 2 y = x - 6$

$\text{subtract 2y from both sides}$

$\cancel{2 y} \cancel{- 2 y} = x - 2 y - 6$

$\Rightarrow x - 2 y - 6 = 0$

$\text{add 6 to both sides}$

$x - 2 y \cancel{- 6} \cancel{+ 6} = 0 + 6$

$\Rightarrow x - 2 y = 6 \leftarrow \textcolor{red}{\text{in standard form}}$

Mar 22, 2018

$x - 2 y = 6$

#### Explanation:

The standard form for a linear equation is:

$A x + B y = C$,

where if at all possible:

$A , B , \mathmr{and} C$ are integers, and $A$ is non-negative, and $A , B , \mathmr{and} C$ have no common factors other than 1.
http://courses.wccnet.edu/~palay/precalc/22mt01.htm

$y = \frac{1}{2} x - 3$ is in slope-intercept form. To convert to standard form, subtract $\frac{1}{2} x$ from both sides.

$- \frac{1}{2} x + y = - 3$

Multiply both sides by $- 2$.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} \left(- \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} x\right) + - 2 \left(y\right) = - 3 \times - 2$

Simplify.

$x - 2 y = 6$