# How do you write the standard form of a line given slope= -5, passes through (-3, -8)?

Aug 11, 2016

$y = - 5 x - 23$

#### 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 = - 5 and $\left({x}_{1} , {y}_{1}\right) = \left(- 3 , - 8\right)$

substitute these values into the equation.

$\Rightarrow y - \left(- 8\right) = - 5 \left(x - \left(- 3\right)\right) \Rightarrow y + 8 = - 5 \left(x + 3\right)$

distribute bracket and collect 'like terms'

$\Rightarrow y + 8 = - 5 x - 15 \Rightarrow y = - 5 x - 23$