How do you write an equation in standard form given point (0,0) and slope 1/3?

Dec 29, 2017

$1 x - 3 y = 0$

Explanation:

For a line with slope $\textcolor{g r e e n}{\frac{1}{3}}$ through the point $\left(x , y\right) = \left(\textcolor{red}{0} , \textcolor{b l u e}{0}\right)$
the slope-point form is
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{0} = \textcolor{g r e e n}{\frac{1}{3}} \left(x - \textcolor{red}{0}\right)$
which simplifies as
$\textcolor{w h i t e}{\text{XXX}} 3 y = 1 x$

Standard form for a linear equation is
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$ with $A , B , C \in \mathbb{Z}$ and $A \ge 0$

To convert $3 y = 1 x$ into standard form
subtract $3 y$ from both sides:
$\textcolor{w h i t e}{\text{XXX}} 0 = 1 x - 3 y$
then reverse the left and right hand sides
$\textcolor{w h i t e}{\text{XXX}} 1 x - 3 y = 0$