# How do you write an equation in slope intercept form given that the line passes through (-2,-1) and (3,-4)?

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;

$\frac{- 4 - \left(- 1\right)}{3 - \left(- 2\right)} = - \frac{3}{5}$

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

We should use one point to find the real equation. If we use (3,-4) point;
$y = a x + b \implies - 4 = 3 a + b$;
a is the slope of the equation, we found that as $- \frac{3}{5}$;
$- 4 = \left(3 \cdot - \frac{3}{5}\right) + b \implies - 4 = - \frac{9}{5} + b \implies b = - 4 + \frac{9}{5} = \frac{- 20 + 9}{5} \implies b = - \frac{11}{5}$;
So the equation of the line will be;
$y = a x + b \implies \underline{y = - \frac{3}{5} x - \frac{11}{5}}$
We can check if our equation is right or not with other given point;
$\left(- 2 , - 1\right) \implies y = - \frac{3}{5} x - \frac{11}{5} \implies - 1 = - \frac{3}{5} \cdot \left(- 2\right) - \frac{11}{5} \implies - 1 = \frac{6}{5} - \frac{11}{5} \implies - 1 = - \frac{5}{5} \implies - 1 = - 1$
So the equation is correct :)