Successfully reported this slideshow.
Upcoming SlideShare
×

# Parallel lines

596 views

Published on

This tutorials helps you to find out the parallel and perpendicular lines. In this section, the slope of the parallel lines are equal and the slope of perpendicular lines are negative reciprocal to each other or product of slopes equation to -1.
If you have any query about math problems, feel free to contact www.freematheducation.com

Published in: Technology
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

### Parallel lines

1. 1. WELCOME TOTOPIC : Parallel Lines The online version of this tutorial can be accessed at www.freematheducation.com. It provides all the basics and the concept in details including more practice questions with complete step by step solutions. In case you have any questions about algebra course outline, please feel free to contact us at krtis816@gmail.com or call +91-94612-01100 (INDIA) www.freematheducation.com 1 :
2. 2. Parallel LinesTwo lines with the same slope are said to be a parallel lines. When we plot agraph of parallel lines then they will never intersect to each other. A B C DLine AB and Line CD are Parallel lines and it is denoted by AB||CD.The equation of the straight lines are y = m1x + c and y = m2x + c are parallel ifthe slopes of both lines are equal i.e. m1 = m2 www.freematheducation.com www.freematheducation.com 2 :
3. 3. Parallel LinesQ. Are the lines 12x + 3y = – 9 and – 8x – 2y = 14 are parallel?Solution:First find the slope of both the lines 12x + 3y = – 9 –8x – 2y = 14 y = –4x – 3 3y = –12x – 9 –2y = 8x + 14 y = –4x – 3 y = –4x – 7 Slope = –4 Slope = –4 y = –4x – 7Since the slopes of both the lines are equal, so the lines are parallel. www.freematheducation.com www.freematheducation.com 3 :
4. 4. Parallel LinesPractice Question :Are the given lines are parallel?1. 6x – 3y = 5 and 2y = 4x – 42. x + 2y = 6 and 2x – 2y = 63. 5x – y = 5 and y = 10x – 44. 3x – 3y = 6 and x – y = 6 www.freematheducation.com www.freematheducation.com 4 :
5. 5. WELCOME TOTOPIC : Constructing Parallel Lines The online version of this tutorial can be accessed at www.freematheducation.com . It provides all the basics and the concept in details including more practice questions with complete step by step solutions. In case you have any questions about algebra course outline, please feel free to contact us at krtis816@gmail.com or call +91-94612-01100 (INDIA) www.freematheducation.com 5 :
6. 6. Constructing Parallel LinesWe can find the equation of a line parallel to the a given line which is passingthrough the point by  finding the slope m of the given line;  Finding the equation of a line through the given point (x1, y1) with the slope equals to m.The slope intercept form of a line is y = mx + c, where m is the slope of the lineand c be its y intercept.The equation of a line passing through point (x1, y1) with slope m is given by y – y1 = m (x – x1) www.freematheducation.com www.freematheducation.com 6 :
7. 7. Constructing Parallel LinesQ. Find the equation of a line which is parallel to the line 2x + 6y = 12 andpassing through point (2, –1).Solution:To find the equation of a line, first find the slope of given line 6x + 2y = 12 Compare with 2y = – 6x + 12 Slope Intercept Form y = – 3x + 6 y = mx + c Slope = –3The slope of a line is -3. Since the slopes of parallel lines are equal. Thereforethe equation of a line is given by y – y1 = m (x – x1) y – (–1) = –3 (x – 2) y + 1= –3x + 6 3x + y = 5 www.freematheducation.com www.freematheducation.com 7 :
8. 8. Constructing Parallel LinesPractice Question :1. Find the equation of the line going through the point (4, –1) and parallel to x + 2y = 102. Find the equation of the line going through the point (–2, –7) and parallel to 2x – 3y = 12 www.freematheducation.com www.freematheducation.com 8 :
9. 9. WELCOME TOTOPIC : Perpendicular Lines The online version of this tutorial can be accessed at www.freematheducation.com . It provides all the basics and the concept in details including more practice questions with complete step by step solutions. In case you have any questions about algebra course outline, please feel free to contact us at krtis816@gmail.com or call +91-94612-01100 (INDIA) www.freematheducation.com 9 :
10. 10. Perpendicular LinesPerpendicular lines are the lines that intersect in a right angle.We can find the equation of a line perpendicular to a given line and goingthrough a given point by:  finding the slope m of the given line;  Finding the equation of a line through the given point (x1, y1) with the slope equals to -1/m.The slope intercept form of a line is y = mx + c, where m is the slope of the lineand c be its y intercept.The equation of a line passing through point (x1, y1) with slope m is given by y – y1 = m (x – x1)The equation of the straight lines are y = m1x + c and y = m2x + c areperpendicular the slopes are negative reciprocal to each other i.e. m1m2 = -1. www.freematheducation.com www.freematheducation.com 10 :
11. 11. Perpendicular LinesQ. Are the lines 2x + y = 5 and x – 2y = – 4 are perpendicular?Solution:First find the slope of both the lines 2x + y = 5 x – 2y = –4 2x + y = 5 y = –2x + 5 –2y = –x – 4 y = ½ x +2 Slope m1 = –2 Slope m2 = ½ x – 2y = – 4 m1 m2 = –2 x ½ = –1Since the slopes of both the lines are negative reciprocal to each other, so boththe lines are perpendicular lines. www.freematheducation.com www.freematheducation.com 11 :
12. 12. Perpendicular LinesPractice Question :Are the given lines are parallel?1. 6x – 3y = 5 and 3x + 6y = 142. 3x – 3y = 6 and 3x + 3y = 83. x + 2y = 6 and x – 2y = 64. y = 10x – 12 and y = 10x – 4 www.freematheducation.com www.freematheducation.com 12 :
13. 13. WELCOME TOTOPIC : Constructing Perpendicular Lines The online version of this tutorial can be accessed at www.freematheducation.com . It provides all the basics and the concept in details including more practice questions with complete step by step solutions. In case you have any questions about algebra course outline, please feel free to contact us at krtis816@gmail.com or call +91-94612-01100 (INDIA) www.freematheducation.com 13 :
14. 14. Constructing Perpendicular LinesWe can find the equation of a line perpendicular to the given line which ispassing through the point by  finding the slope m1 of the given line;  Find the negative reciprocal of that slope i.e. m2 = 1/m1  Finding the equation of a line through the given point (x1, y1) with the slope equals to m2.The slope intercept form of a line is y = mx + c, where m is the slope of the lineand c be its y intercept.The equation of a line passing through point (x1, y1) with slope m2 is given by y – y1 = m2 (x – x1) www.freematheducation.com www.freematheducation.com 14 :
15. 15. Constructing Perpendicular LinesQ. Find the equation of a line given through the point (3, 0) and perpendicularto 6x + 2y = 12.Solution:To find the equation of a line, first find the slope of given line 6x + 2y = 12 Compare with 2y = – 6x + 12 y = – 3x + 6 Slope Intercept Form y = mx + c Slope = –3Slope of perpendicular line is m2 = –(1/ –3) = 1/3. Therefore the equation of aline perpendicular to given line is y – y1 = m2 (x – x1) y – (0) = 1/3 (x – 3) y = –1/3 x – 1 x + 3y + 3 = 0 www.freematheducation.com www.freematheducation.com 15 :
16. 16. Constructing Perpendicular LinesPractice Question :1. Find the equation of the line going through the point (4, –1) and perpendicular to x + 2y = 10.2. Find the equation of the line going through the point (–2, –7) and perpendicular to 2x – 3y = 12 www.freematheducation.com www.freematheducation.com 16 :
17. 17. WELCOME TOTOPIC : Answer Key The online version of this tutorial can be accessed at www.freematheducation.com . It provides all the basics and the concept in details including more practice questions with complete step by step solutions. In case you have any questions about algebra course outline, please feel free to contact us at krtis816@gmail.com or call +91-94612-01100 (INDIA) www.freematheducation.com 17 :
18. 18. Answer KeyYour practice Session is completed. Your Answer Key isParallel Lines : 1. Yes 2. No 3. No 4. YesConstructing Parallel Lines : 1. x – y = 2 2. 2x – 3y = 17Perpendicular Lines : 1. Yes 2. Yes 3. No 4. NoConstructing Perpendicular Lines : 1. 2x – y = 9 2. 3x + 2y = – 20 www.freematheducation.com www.freematheducation.com 18 :
19. 19. Parallel Lines Thanks For Visiting www.freematheducation.comIn case you have any questions about algebra course outline, please feel free tocontact us at krtis816@gmail.com or call +91-94612-01100 We would love to hear from you! www.freematheducation.com www.freematheducation.com 19 :