Question

What is the equation of the line passing through the points (–2, 2) and (3, –1)?

Answer 1

First you have to find the slope \[m=(y _{2}-y _{1})/(x _{2}-x _{1})\]
So you will have
\[\frac{ -1-2 }{ 3-(-2) }=\frac{ -3 }{ 5 }\]
So the slope is \[-\frac{ 3 }{ 5 }\]
Now you have to use the point slope formula \[y-y_{1}=m(x-x _{1})\]
So you use one of the points, it doesn't matter which one, and the slope and plug it in.\[y-2=-\frac{ 3 }{ 5 }(x-(-2))\]
Now depending on what the question asked, you might need to clean it up by distributing.

Answer 2

Here is the point-slope formula in one single equation:

\(y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1} (x - x_1)\)