# How do you write an equation of a line given point (-8,5) and m=-2/5?

Jan 15, 2017

See entire explanation below

#### Explanation:

To write an equation for this line give the slope and one point use the point-slope formula.

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the point and slope from the problem gives:

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{- \frac{2}{5}} \left(x - \textcolor{red}{- 8}\right)$

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{- \frac{2}{5}} \left(x + \textcolor{red}{8}\right)$

Or, we can solve for $y$ to put this equation in the more familiar slope-intercept form:

The slope-intercept form of a linear equation is:

$y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and color(blue)(b is the y-intercept value.

$y - \textcolor{red}{5} = \textcolor{b l u e}{- \frac{2}{5}} x + \left(\textcolor{b l u e}{- \frac{2}{5}} \times \textcolor{red}{8}\right)$

$y - \textcolor{red}{5} = \textcolor{b l u e}{- \frac{2}{5}} x - \frac{16}{5}$

$y - \textcolor{red}{5} + 5 = \textcolor{b l u e}{- \frac{2}{5}} x - \frac{16}{5} + 5$

$y - 0 = - \frac{2}{5} x - \frac{16}{5} + \left(\frac{5}{5} \times 5\right)$

$y = - \frac{2}{5} x - \frac{16}{5} + \frac{25}{5}$

$y = - \frac{2}{5} x + \frac{9}{5}$