# What is the slope-intercept form of the line passing through (2, 2)  and (-1, 4) ?

Jun 1, 2016

$- \frac{2}{3}$ is the slope and $\frac{10}{3}$ is the intercept.

#### Explanation:

A line in the plane follow the equation

$y = m x + q$. In this equation we want to calculate the two parameters $m$ and $q$. To do it we substitute the values of $x$ and $y$ and we have a system of equations

$2 = 2 m + q$
$4 = - 1 m + q$

from one of the two equation (for example the first) I write one variable as the other:

$2 = 2 m + q$ then $q = 2 - 2 m$

and now substitute this in the other equation

$4 = - m + q$ then $4 = - m + 2 - 2 m$
$4 = 2 - 3 m$
$4 - 2 = - 3 m$
$2 = - 3 m$
$m = - \frac{2}{3}$

to find $q$ I take the $q = 2 - 2 m$ and substitute the value of $m$

$q = 2 - 2 \left(- \frac{2}{3}\right) = 2 + \frac{4}{3} = \frac{10}{3}$

The line has equation

$y = - \frac{2}{3} x + \frac{10}{3}$ where $- \frac{2}{3}$ is the slope and $\frac{10}{3}$ is the intercept.