# What is the slope-intercept form of the line passing through  (-2, -1) and  (0, -6) ?

May 2, 2017

See the entire solution process below:

#### Explanation:

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.

First 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:

$m = \frac{\textcolor{red}{- 6} - \textcolor{b l u e}{- 1}}{\textcolor{red}{0} - \textcolor{b l u e}{- 2}} = \frac{\textcolor{red}{- 6} + \textcolor{b l u e}{1}}{\textcolor{red}{0} + \textcolor{b l u e}{2}} = - \frac{5}{2}$

The point $\left(0 , - 6\right)$ is the y-intercept (the value of $y$ when $x$ is $0$).

Substituting the slope we calculated and the y-intercept gives:

$y = \textcolor{red}{- \frac{5}{2}} x + \textcolor{b l u e}{- 6}$

$y = \textcolor{red}{- \frac{5}{2}} x - \textcolor{b l u e}{6}$