# How do you find a standard form equation for the line with point (5, 0), and whose slope is -2?

Feb 20, 2017

See the entire solution process below:

#### Explanation:

First, we can use the point-slope formula to write 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 slope and point from the problem gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{- 2} \left(x - \textcolor{red}{5}\right)$

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 equation we obtained above into the form as follows:

$y = \left(\textcolor{b l u e}{- 2} \times x\right) - \left(\textcolor{b l u e}{- 2} \times \textcolor{red}{5}\right)$

$y = - 2 x + 10$

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

$2 x + y = 0 + 10$

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