# How do you write the slope-intercept form of the line with (-5,0) and (8,-4)?

Jul 23, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{0}}{\textcolor{red}{8} - \textcolor{b l u e}{- 5}} = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{0}}{\textcolor{red}{8} + \textcolor{b l u e}{5}} = - \frac{4}{13}$

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.

We can solve for $\textcolor{b l u e}{b}$ by substituting the slope we just calculated and one of the points in the problem for $x$ and $y$:

$0 = \left(\textcolor{red}{- \frac{4}{13}} \cdot - 5\right) + \textcolor{b l u e}{b}$

$0 = \frac{20}{13} + \textcolor{b l u e}{b}$

$0 - \frac{20}{13} = \frac{20}{13} - \frac{20}{13} + \textcolor{b l u e}{b}$

$- \frac{20}{13} = 0 + \textcolor{b l u e}{b}$

#-20/13 = color(blue)(b)

We can substitute the slope we calculated and the value of $\textcolor{red}{b}$ we calculated into the formula to write the equation of the line.

$y = \textcolor{red}{- \frac{4}{13}} x + \textcolor{b l u e}{- \frac{20}{13}}$

$y = \textcolor{red}{- \frac{4}{13}} x - \textcolor{b l u e}{\frac{20}{13}}$