# How do you write the equation in standard form given m = -1/2 and (4,6)?

Jan 31, 2017

$x + 2 y - 16 = 0$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{standard form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{a x + b y + c = 0} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where a is a positive integer and b, c are integers.

Begin by expressing the equation in $\textcolor{b l u e}{\text{point-slope form}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ is a point on the line}$

$\text{here "m=-1/2" and } \left({x}_{1} , {y}_{1}\right) = \left(4 , 6\right)$

Substituting these values into the equation.

$y - 6 = - \frac{1}{2} \left(x - 4\right) \leftarrow \textcolor{red}{\text{point-slope form}}$

distributing, simplifying and rearranging.

$y - 6 = - \frac{1}{2} x + 2$

$\Rightarrow \frac{1}{2} x + y - 8 = 0$

coefficient of x, that is a must be an integer.

multiplying through by 2

$\Rightarrow x + 2 y - 16 = 0 \leftarrow \textcolor{red}{\text{ in standard form}}$