# What is the equation of the line with slope  m= -13/5  that passes through  (-23,16) ?

Apr 17, 2017

See the entire solution process below:

#### Explanation:

We can use the point-slope formula to find the equation of the line meeting the criteria in the problem. 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 slope and values for the point from the problem gives:

$\left(y - \textcolor{red}{16}\right) = \textcolor{b l u e}{- \frac{13}{5}} \left(x - \textcolor{red}{- 23}\right)$

$\left(y - \textcolor{red}{16}\right) = \textcolor{b l u e}{- \frac{13}{5}} \left(x + \textcolor{red}{23}\right)$

We can also solve for $y$ to find the equation in 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 $\textcolor{b l u e}{b}$ is the y-intercept value.

$y - \textcolor{red}{16} = \left(\textcolor{b l u e}{- \frac{13}{5}} \times x\right) + \left(\textcolor{b l u e}{- \frac{13}{5}} \times \textcolor{red}{23}\right)$

$y - \textcolor{red}{16} = - \frac{13}{5} x - \frac{299}{5}$

$y - \textcolor{red}{16} + 16 = - \frac{13}{5} x - \frac{299}{5} + 16$

$y - 0 = - \frac{13}{5} x - \frac{299}{5} + \left(16 \times \frac{5}{5}\right)$

$y = - \frac{13}{5} x - \frac{299}{5} + \frac{80}{5}$

$y = \textcolor{red}{- \frac{13}{5}} x - \textcolor{b l u e}{\frac{219}{5}}$