# How do you write the standard form of a line given (-2, 4) and has a slope of 1/2?

Aug 15, 2016

$y = \frac{x}{2} + 5$

#### Explanation:

$m : \text{slope of line}$
$P : \left(x , y\right) \text{any point of line}$

$\text{the standard line equation is } y - {y}_{1} = m \left(x - {x}_{1}\right)$

$\text{given " m=1/2" ; "P(-2,4)" ; "y_1=4" ; } {x}_{1} = - 2$

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

$y - 4 = \frac{x}{2} + 1$

$y = \frac{x}{2} + 1 + 4$

$y = \frac{x}{2} + 5$

Aug 15, 2016

$y = \frac{1}{2} x + 5$

#### Explanation:

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

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

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

substitute these values into the equation.

$\Rightarrow y - 4 = \frac{1}{2} \left(x + 2\right)$

distribute the bracket and collect 'like terms'

$y - 4 = \frac{1}{2} x + 1 \Rightarrow y = \frac{1}{2} x + 5 \text{ is the equation}$