# How do you write a equation of a line through point (-6,4) and has a slope of -5/2?

Mar 15, 2017

$y = - \frac{5}{2} x - 11$

#### 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 $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here "m=-5/2" and } \left({x}_{1} , {y}_{1}\right) = \left(- 6 , 4\right)$

$\Rightarrow y - 4 = - \frac{5}{2} \left(x - \left(- 6\right)\right)$

$\Rightarrow y - 4 = - \frac{5}{2} \left(x + 6\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

distributing the bracket and simplifying gives an alternative version of the equation.

$y - 4 = - \frac{5}{2} x - 15$

$\Rightarrow y = - \frac{5}{2} x - 15 + 4$

$\Rightarrow y = - \frac{5}{2} x - 11 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$