Lines in the Plane and Slope

Introduction

The simplest mathematical model for relating two variables is the linear equation $y=mx+b$. This equation is called Linear because its graph is a line. $m$ is the slope and $(0,b)$ is the y-intercept.

Finding the slope $m$

For instance, suppose you want to find the slope of the line passing through the distinct points $(x_{1},x_{2})$ and $(y_{1},y_{2})$.

$Slope={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}={\frac {y_{1}-y_{2}}{x_{1}-x_{2}}}$

Exercises Find the slope of the line passing through the distinct points below

1) $(-3,2)$ and $(3,20)$

Solution:
$4$

2) 3)

Notes:

A vertical line goes through has equation of the form $x=a$ where $a$ is any constant.