# How do you write an equation in standard form given point (-3,-2) and slope 2?

Jun 7, 2017

See a solution process below:

#### Explanation:

First, we can write an equation in the point-slope form. 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 and values from the point in the problem gives:

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

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

We can now transform this equation into the Standard Linear form. 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.

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

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

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

$y + 0 = 2 x + 4$

$y = 2 x + 4$

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

$- 2 x + y = 0 + 4$

$- 2 x + y = 4$

$\textcolor{red}{- 1} \left(- 2 x + y\right) = \textcolor{red}{- 1} \times 4$

$\left(\textcolor{red}{- 1} \times - 2 x\right) + \left(\textcolor{red}{- 1} \times y\right) = - 4$

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