# What is the equation of the line with slope  m= -1  that passes through  (-2,11) ?

Oct 2, 2016

$y = - x + 9$

#### Explanation:

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

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

here m = - 1 and $\left({x}_{1} , {y}_{1}\right) = \left(- 2 , 11\right)$

$\Rightarrow y - 11 = - 1 \left(x + 2\right)$

simplifying.

$y - 11 = - x - 2$

$\Rightarrow y = - x + 9 \text{ is the equation of the line}$