Lydia Baik Period 1
 <center><font size=7> 2.2.1. Slope</font></center> <br>
<b><font color="blue"><font size=4>How do I find slope, given two points?</font></font></b><br>

<b>First here are somethings you should know...</b><br>

*The slope of a nonvertical line is the ratio of vertical change to horizontal change or in simpler terms, rise over run.<br>
*The slope of a line is represented by the letter <b>m</b><br><br>

<b>Take a look here!</b><br>

<img src="http://img99.imageshack.us/img99/1449/graph1tm0.png"></img><br>

The slope of the nonvertical line passing through the points (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>2</sub>) is:<br>

<img src="http://img517.imageshack.us/img517/442/risede0.png"></img><br><br>

<b>Example</b><br>
Find the slope of the line passing through (-2, 4) and (7, 3).<br>
<b>solution:</b>  Let (x<sub>1</sub>, y <sub>1</sub>) = (-2, 4) and (x <sup>2</sup>, y<sup>2</sup>)=(7, 3)<br>
<img src="http://img106.imageshack.us/img106/5526/runvq4.png"></img><br><br>

<b>Now you try!</b><br>
a. Find the slope of the  line passing through (-6 , 2) and (0, 6).<br>

b. Find the slope of the  line passing through (1 , 7) and (-2, -3).<br>

REMEMBER to substitute values then simplify!<br><br>



<b><font color="blue"><font size=4>How do I tell the difference between positive and negative slopes?</font></font></b><br>

<b>First here are somethings you should know...</b><br>
*A line with a positive slope rises from left to right (m>0).<br>
*A line with a negative slope falls from left to right (m<0).<br><br>

<b>Take a look here!</b><br>

<img src="http://img86.imageshack.us/img86/3826/slopeupdo1.png"></img><br>
This  line has a positive slope.<br>

<img src="http://img86.imageshack.us/img86/3310/slopedownzc3.png"></img><br>
This  line has a negative slope. <br><br>

<b>But what if I am  not given a graph?!</b><br>
*If you are given points instead  of a graph heres what you do:<br>
-Find the slope of the line<br>
-If the slope is greater than 0 it is a positive slope<br>
-If the slope is less than 0 it is a negative slope<br><br>


<b>Example:</b><br>
Without graphing tell whether the line through (3, -4), (1, -6) has a positive or negative slope.<br>
<b>solution:</b> Find the Slope of the line.<br>
m = -6 - (-4) / 1-3 = -2/-2 = 1<br>
Because m > 0, the line rises and has a positive slope.<br><br>

<b>Now you try!</b><br>
c. <img src="http://www.purplemath.com/modules/slope/slope01.gif"></img>Positive or Negative?<br>
d. Without graphing tell whether the line through (1, 0), (-4, 6) has a positive or negative slope.<br>

REMEMBER a line with a positive slope rises while a negative slope falls from L to R!<br><br>

<b><font color="blue"><font size=4>How are the slopes of perpendicular lines related?</font></font></b><br>


<b>First here are somethings you should know...</b><br>
* Two lines in a plane that intersect to form a right angle is perpendicular.<br>
*The lines are peperpendicular if and only if their slopes are negative reciprocals of each other.<br><br>
<b>Take a look here!</b><br>
Considering two different nonvertical lines l<sub>1</sub> and l<sub>2</sub> 
<br>
<img src="http://img222.imageshack.us/img222/7958/perpvf2.png"><br>

<b><font size=4>m<sub>1</sub> = -1/m<sub>2</sub><br>

 OR m<sub>1</sub>m<sub>2</sub> = -1</b></font><br><br>

<b>Example:</b><br>
Are the these two lines are perpendicular?<br>
-The slopes of the two lines are m<sub>1</sub> = -2/3 and m<sub>2</sub> = 3/2<br>
-You must substitute your given slopes into m<sub>1</sub>*m<sub>2</sub> = -1 <br>
-m<sub>1</sub>*m<sub>2</sub> = -2/3 * 3/2 = -1<br>
-The two lines are perpendicular.<br><br>

<b>Now you try!</b><br> 
e. Are the these lines with slopes of m<sub>1</sub> =1/3 and m<sub>2</sub> =-1/3 perpendicular?<br>
REMEMBER m<sub>1</sub>m<sub>2</sub>= -1<br>