How do you write an equation of a line that passes through the point (-8, -5) and has a slope of -5/4?

Jan 11, 2017

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

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

$\text{here " m=-5/4" and } \left({x}_{1} , {y}_{1}\right) = \left(- 8 , - 5\right)$

substituting these values into the equation.

$y - \left(- 5\right) = - \frac{5}{4} \left(x - \left(- 8\right)\right)$

$\Rightarrow y + 5 = - \frac{5}{4} \left(x + 8\right) \leftarrow \text{ in point-slope form}$

distributing and simplifying gives the equation in an alternative form.

$y + 5 = - \frac{5}{4} x - 10$

$\Rightarrow y = - \frac{5}{4} x - 15 \leftarrow \text{ in slope-intercept form}$