# How do you find a standard form equation for the line with P (36, 1) and having the slope m = - 1/2?

Jun 16, 2017

$x + 2 y = 38$

#### Explanation:

$\text{the equation of a line in "color(blue)"standard form}$ is.

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

$\text{begin by expressing the equation in "color(blue)"point-slope form}$

• y-y_1=m(x-x_1)

$\text{where m represents the slope and " (x_1,y_1)" a point}$

$\text{here " m=-1/2" and } \left({x}_{1} , {y}_{1}\right) = \left(36 , 1\right)$

$\Rightarrow y - 1 = - \frac{1}{2} \left(x - 36\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

$\text{rearrange into standard form}$

$y - 1 = - \frac{1}{2} x + 18 \leftarrow \text{ distributing}$

$\frac{1}{2} x + y = 19 \leftarrow \text{ multipy terms by 2}$

$\Rightarrow x + 2 y = 38 \leftarrow \textcolor{red}{\text{ in standard form}}$