View source for Lines in the Plane and Slope

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

==Finding the slope <math> m </math>==
For instance, suppose you want to find the slope of the line passing through the distinct points <math> (x_1,x_2) </math> and <math> (y_1,y_2) </math>.

<math>Slope =\frac {y_2-y_1}{x_2-x_1} =\frac {y_1-y_2}{x_1-x_2}</math>

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

'''1)''' <math>(-6,2)</math> and <math>(3,20)</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution: &nbsp;
|-
|<math style="vertical-align: -5px">2</math>
|-
|}

'''2)'''<math>(3,-7)</math> and <math>(-3,-7)</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution: &nbsp;
|-
|<math style="vertical-align: -5px">0</math>
|-
|}

'''3)'''<math>(3,-2)</math> and <math>(-3,1)</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution: &nbsp;
|-
|<math style="vertical-align: -5px">\frac {-1}{2}</math>
|-
|}

==Writing the linear equation==

<div class="boxed">
'''Point-Slope Form of the Equation of a Line'''

The equation of the line with slope  passing through the point <math>(x_1,y_1)</math> is 

<math>y-y_1=m(x-x_1)</math>
</div>

==Notes:==
A vertical line goes through has equation of the form <math> x=a </math> where <math> a </math> is any constant.

'''This page were made by [[Contributors|Tri Phan]]'''