3.6+&+3.7+Lines+on+the+Coordinate+Plane

In these sections, you will learn how to find the slope, how to determine if lines are perpendicular, and how to write perpendicular line equations. To find the slope of parallel lines, you put the rise over run, or the change in the y coordinates over the change in the x coordinates.
 * [[image:http://www.wikispaces.com/i/edit.png width="128" height="37" caption="Edit This Page" link="page/edit/3.6 & 3.7 Lines on the Coordinate Plane"]]__3.6 and 3.7 Lines On the Coordinate Plane and Perpendicular lines in a coordinate plane__ ||  ||

Online Textbook pg. 165 Example: Online Textbook pg 165
 * Let (//x//1, //y//1) = ( 0, 6 ) and (//x//2, //y//2) = ( 5 , 2 ).[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8" caption="external image blank.gif"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11" caption="external image blank.gif"]] ||


 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/mcd_ma_geo_lsn_0395937779_p165_f07.gif align="top" caption="external image mcd_ma_geo_lsn_0395937779_p165_f07.gif"]][[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8" caption="external image blank.gif"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11" caption="external image blank.gif"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/bluesquare.gif align="absmiddle" caption="external image bluesquare.gif"]] The slope of the line is –[[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_4_5.gif align="absmiddle" caption="external image frac_4_5.gif"]]. ||

To determine if a line is perpendi cular, you must find the slopes of both lines, and multiply them. If the product of the two slopes is -1 and ONLY -1. If this is not the product, then the two lines are not perpendicular.

Example:

Online textbook pg 172.



//**Multiply**// the slopes.



Writing equations of perpendicular lines Line 1 has equation //y// = –2 //x// + 1. Find an equation of the line 2 that passes through //P//(4, 0) and is perpendicular to 1. First you must find the slope, //m//2.

 Then use //m// = and (//x//, //y//) = (4, 0) to find //b//.

 When you write an equation of a parallel line, the slope ALWAYS stays the same, no matter what, and when you are given a point and your slope to write an equation parallel just follow these steps: you have to solve for your y intercept, or "b", so you plug in your two points into the equation, and it will lead to what your b equals. then you just plug back the slope and the y intercept into the equation and there you go.a
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/bluesquare.gif align="absmiddle" caption="external image bluesquare.gif"]] So, an equation of [[image:http://images.classwell.com/ebooks/images/mcd_geo/script_l.gif align="middle" caption="external image script_l.gif"]]2 is //y// = [[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_1_2.gif align="middle" caption="external image frac_1_2.gif"]]//x// – 2 . ||
 * Writing an Equation of a Parallel Line ||
 * Line //n//1 has the equation //y// = –[[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_1_3.gif align="middle"]]//x// – 1.

Line //n//2 is parallel to //n//1 and passes through the point (3, 2). Write an equation of //n//2.

Online textbook page 167.


 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] || //**Find**// the slope.[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||


 * The slope of //n//1 is –[[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_1_3.gif align="middle"]]. Because parallel lines have the same slope, the slope of //n//2 is also –[[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_1_3.gif align="middle"]].[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||


 * //**Solve**// for //b//. Use (//x//, //y//) = (3, 2) and //m// = –[[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_1_3.gif align="absmiddle"]].[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||


 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/mcd_ma_geo_lsn_0395937779_p165_f17.gif align="top"]][[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||


 * //**Write**// an equation.[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/bluesquare.gif align="absmiddle"]] Because //m// = –[[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_1_3.gif align="middle"]] and //b// = 3, an equation of //n//2 is //y// = –[[image:http://images.classwell.com/ebooks/images/mcd_geo/frac_1_3.gif align="middle"]]//x// + 3. ||

WEBSITES http://www.homeschoolmath.net/teaching/g/parallel_and_perpendicular.php http://www.learningwave.com/lwonline/algebra_section2/slope3.html

__extra-practice problems__ 1.Write an equation of the line through the point (2, 3) that has a slope of 5. Math textbook page 167

2 . Online textbook page 173
 * Decide whether the lines are perpendicular.



3. The equation //y// = //x// + 3 represents a mirror. A ray of light hits the mirror at (–2, 0). What is the equation of the line //p// that is perpendicular to the mirror at this point?

Math textbook page 174

answers:

1.//y// = 5//x// – 7

2.Yes, the lines are perpendicular.

3.//y// = –//x// –. ||