# How do you write an equation of a line with point (2,5) and slope -2?

Nov 12, 2016

$y = - 2 x + 9$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

here $m = - 2 \text{ and } \left({x}_{1} , {y}_{1}\right) = \left(2 , 5\right)$

substitute these values into the equation.

$\Rightarrow y - 5 = - 2 \left(x - 2\right)$

distribute the bracket and collect like terms.

$y - 5 = - 2 x + 4 \Rightarrow y = - 2 x + 4 + 5$

$\Rightarrow y = - 2 x + 9 \text{ is the equation}$