# How do you write the equation of a line in point slope form and slope intercept form given points (-3, 2) and (2, 1)?

May 30, 2015

First we have to find the slope of the equation. To find the slope we have to do;
$\frac{y 2 - y 1}{x 2 - x 1}$ For our question slope is;

$\frac{1 - 2}{2 - \left(- 3\right)} = - \frac{1}{5}$

The main formula of a line is;
$y = a x + b$

We should use one point to find the real equation. If we use (2,1) point;
$y = a x + b \implies 1 = 2 a + b$;
a is the slope of the equation, we found that as $- \frac{1}{5}$;
$1 = \left(2 \cdot - \frac{1}{5}\right) + b \implies 1 = - \frac{2}{5} + b \implies b = 1 + \frac{2}{5} \implies b = \frac{7}{5}$;
So the equation of the line will be;
$y = a x + b \implies \underline{y = - \frac{x}{5} + \frac{7}{5}}$
We can check if our equation is right or not with other given point;
$\left(- 3 , 2\right) \implies y = - \frac{x}{5} + \frac{7}{5} \implies 2 = - 3 \cdot \left(- \frac{1}{5}\right) + \frac{7}{5} \implies 2 = \frac{3}{5} + \frac{7}{5} \implies 2 = \frac{10}{5} \implies 2 = 2$
So the equation is correct :)