How do you write an equation in point-slope form for the given (-3, 2) and (2, 1)?

Aug 4, 2015

Determine the slope between the given points and then plug it and one of the point coordinates into the general point-slope form to get:
$\textcolor{w h i t e}{\text{XXXX}}$$\left(y - 1\right) = - \frac{1}{5} \left(x - 2\right)$

Explanation:

Determine slope between $\left(- 3 , 2\right)$ and $\left(2 , 1\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{\Delta y}{\Delta x} = \frac{2 - 1}{- 3 - 2} = - \frac{1}{5}$

Insert values into point-slope form
The general point-slope form is
$\textcolor{w h i t e}{\text{XXXX}}$$\left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$
Using the calculated slope and the point $\left(2 , 1\right)$ this becomes
$\textcolor{w h i t e}{\text{XXXX}}$$\left(y - 1\right) = - \frac{1}{5} \left(x - 2\right)$