# How do you write the standard form of the equation given (-2,5) and slope -4?

Sep 7, 2017

$y = - 4 x - 3$

#### Explanation:

The given values of $\left(- 2 , 5\right)$ and $- 4$ represent $x , y \mathmr{and} m$ in
$y = m x + c$, which is the equation of a straight line.

Substitute these values to find the value of $c$, the $y$-intercept.

$y = m x + c$

$5 = \left(- 4\right) \left(- 2\right) + c$

$5 = 8 + c$

$5 - 8 = c$

$- 3 = c$

The required equation is:

$y = - 4 x - 3$

Sep 7, 2017

$4 x + y = - 3$

#### Explanation:

$\text{the standard form of the equation of a line is}$

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

$\text{we can establish the equation in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{here } m = - 4$

$\Rightarrow y = 4 x + b \leftarrow \text{ partial equation}$

$\text{to find b substitute "(-2,5)" into the equation}$

$5 = 8 + b \Rightarrow b = - 3$

$\Rightarrow y = - 4 x - 3 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$

$\Rightarrow 4 x + y = - 3 \leftarrow \textcolor{red}{\text{ in standard form}}$