# How do you find a standard form equation for the line with origin with slope -6?

Feb 16, 2017

See the entire solution process below:

#### Explanation:

If the line has the origin, (0, 0), as a point on the line and a slope of $- 6$ we can use the point-slope formula to find an equation for the line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the slope given in the problem and the origin gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{- 6} \left(x - \textcolor{red}{0}\right)$

$y = - 6 x$

We can convert this to the standard form for a linear equation. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

We will add $\textcolor{red}{6 x}$ to each side of the equation to start the conversion and keep the equation balanced:

$\textcolor{red}{6 x} + y = \textcolor{red}{6 x} - 6 x$

$6 x + y = 0$

Or

$\textcolor{red}{6} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{0}$