How do you find the slope intercept form of the equation of the line with y-intercept(0,-2) and x intercept(8,0)?

Jan 31, 2017

See the entire solution process below:

Explanation:

First we need to determine the slope from the two points provided in the problem. 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 value from the points and calculating gives:

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

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

$m = \frac{2}{8} = \frac{1}{4}$

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 value from the y-intercept given in the problem results in:

$y = \textcolor{red}{\frac{1}{4}} x + \textcolor{b l u e}{- 2}$

$y = \textcolor{red}{\frac{1}{4}} x - \textcolor{b l u e}{2}$