# How do you write the standard form of a line given (-3, -10) and has a slope of 2?

Feb 5, 2017

$\textcolor{red}{2} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{4}$

#### Explanation:

First, use the point-slope formula to write 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 information from the problem gives:

$\left(y - \textcolor{red}{- 10}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{- 3}\right)$

$\left(y + \textcolor{red}{10}\right) = \textcolor{b l u e}{2} \left(x + \textcolor{red}{3}\right)$

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

Transform the equation from point-slope to standard form as follows:

$y + \textcolor{red}{10} = \left(\textcolor{b l u e}{2} \times x\right) + \left(\textcolor{b l u e}{2} \times \textcolor{red}{3}\right)$

$y + \textcolor{red}{10} = 2 x + 6$

$- \textcolor{red}{2 x} + y + \textcolor{red}{10} - 10 = - \textcolor{red}{2 x} + 2 x + 6 - 10$

$- \textcolor{red}{2 x} + y + 0 = 0 - 4$

$- 2 x + y = - 4$

$- 1 \left(- 2 x + y\right) = - 1 \times - 4$

$2 x - y = 4$