# What is the slope intercept form of the line passing through (2,-7)  with a slope of -1/3 ?

Sep 1, 2016

$y = - \frac{1}{3} x + \left(- \frac{19}{3}\right)$

#### Explanation:

Start with the slope-point form: $y - \textcolor{b l u e}{b} = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{a}\right)$
for a line with slope $\textcolor{g r e e n}{m}$ and a point $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

Given color(green)(m)=color(green)(-1/3
and point $\left(\textcolor{red}{2} , \textcolor{b l u e}{- 7}\right)$

We have
$\textcolor{w h i t e}{\text{XXX}} y + \textcolor{b l u e}{7} = \textcolor{g r e e n}{- \frac{1}{3}} \left(x - \textcolor{red}{2}\right)$

The slope-intercept form is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} x + \textcolor{p u r p \le}{k}$
with the y-intercept at $\textcolor{p u r p \le}{k}$

Converting $y + \textcolor{b l u e}{7} = \textcolor{g r e e n}{- \frac{1}{3}} \left(x - \textcolor{red}{2}\right)$
into slope-intercept form:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{- \frac{1}{3}} \left(x - \textcolor{red}{2}\right) - \textcolor{b l u e}{7}$

$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{- \frac{1}{3}} x + \frac{2}{3} - \frac{7 \cdot 3}{3}$

$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{- \frac{1}{3}} x + \left(\textcolor{p u r p \le}{- \frac{19}{3}}\right)$

Here is what it looks like as a graph:
graph{-1/3x-19/3 [-5.277, 3.492, -8.528, -4.144]}