# How do you find a standard form equation for the line with (-3,6) M = -2?

Feb 16, 2017

See the entire solution process below:

#### Explanation:

We can use the point slope formula to first find an equation for this 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 values from the problem gives:

$\left(y - \textcolor{red}{6}\right) = \textcolor{b l u e}{- 2} \left(x - \textcolor{red}{- 3}\right)$

$\left(y - \textcolor{red}{6}\right) = \textcolor{b l u e}{- 2} \left(x + \textcolor{red}{3}\right)$

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 can convert the point-slope form to the standard form as follows:

$y - \textcolor{red}{6} = \left(\textcolor{b l u e}{- 2} \times x\right) + \left(\textcolor{b l u e}{- 2} \times \textcolor{red}{3}\right)$

$y - \textcolor{red}{6} = - 2 x - 6$

$\textcolor{b l u e}{2 x} + y - \textcolor{red}{6} + 6 = \textcolor{b l u e}{2 x} - 2 x - 6 + 6$

$2 x + y - 0 = 0 - 0$

$\textcolor{red}{2} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{0}$