# What is the equation of the line passing through (8,4) and (0,-2)?

Aug 29, 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:

$m = \frac{\textcolor{red}{- 2} - \textcolor{b l u e}{4}}{\textcolor{red}{0} - \textcolor{b l u e}{8}} = \frac{- 6}{-} 8 = \frac{3}{4}$

We know from the point $\left(0 , - 2\right)$ the $y$-intercept is $- 2$. The $y$-intercept is the point where $x = 0$ and the line crosses the $y$-axis.

We can use the slope-intercept formula to write and equation for the line. 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.

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

$y = \textcolor{red}{\frac{3}{4}} x + \textcolor{b l u e}{\left(- 2\right)}$

$y = \textcolor{red}{\frac{3}{4}} x - \textcolor{b l u e}{2}$