Lines in the Plane and Slope

Introduction

The simplest mathematical model for relating two variables is the linear equation $y=mx+b$ (Slope-intercept form). 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 (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 $(-3,1)$

Solution:
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (x_{1},y_{1})}
 is 

 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 y-y_1=m(x-x_1)}

Notice: In order to write this equation, we need a point and a slope given

Notes:

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

This page were made by Tri Phan