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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (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) $(-6,2)$ and $(3,20)$

Solution:
$2$

2)$(3,-7)$ and $(-3,-7)$

Solution:
$0$

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

Solution:
${\frac {-1}{2}}$

Writing the linear equation

Point-Slope Form of the Equation of a Line The equation of the line with slope passing through the point $(x_{1},y_{1})$ is

$y-y_{1}=m(x-x_{1})$

Notes:

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

This page were made by Tri Phan