# How do you write an equation in point slope and slope intercept form given point (8,0), m=1/3?

Feb 4, 2017

Point-slope form: $\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{1}{3}} \left(x - \textcolor{red}{8}\right)$

Slope-intercept form: $y = \textcolor{red}{\frac{1}{3}} x - \textcolor{b l u e}{\frac{8}{3}}$

#### Explanation:

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 point and slope from the problem gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{1}{3}} \left(x - \textcolor{red}{8}\right)$

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 the point-slope form of the equation for $y$ to obtain the slope-intercept form:

$y - \textcolor{red}{0} = \left(\textcolor{b l u e}{\frac{1}{3}} \times x\right) - \left(\textcolor{b l u e}{\frac{1}{3}} \times \textcolor{red}{8}\right)$

$y = \frac{1}{3} x - \frac{8}{3}$