# How do you write an equation in standard form given point (4,2) and slope -2?

##### 1 Answer
Apr 23, 2017

See the entire solution process below:

#### Explanation:

We can 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 slope and the values from the point in the problem gives.

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{- 2} \left(x - \textcolor{red}{4}\right)$

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 now transform the point-slope equation to standard form as follows:

$y - \textcolor{red}{2} = \left(\textcolor{b l u e}{- 2} \cdot x\right) - \left(\textcolor{b l u e}{- 2} \cdot \textcolor{red}{4}\right)$

$y - \textcolor{red}{2} = - 2 x + 8$

$\textcolor{b l u e}{2 x} + y - \textcolor{red}{2} + 2 = \textcolor{b l u e}{2 x} - 2 x + 8 + 2$

$2 x + y - 0 = 0 + 10$

$\textcolor{red}{2} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{10}$