Lines in the Plane and Slope

Introduction

The simplest mathematical model for relating two variables is the linear equation Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y=mx+b} . This equation is called Linear because its graph is a line. Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle m} is the slope and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (0,b)} is the y-intercept.

Finding the slope Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle m}

For instance, suppose you want to find the slope of the line passing through the distinct points Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (-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