Equations of Parallel and Perpendicular Lines ALGEBRA 1
![Equations of Parallel and Perpendicular Lines ALGEBRA 1 UNIT 5: WRITING EQUATIONS OF LINES Equations of Parallel and Perpendicular Lines ALGEBRA 1 UNIT 5: WRITING EQUATIONS OF LINES](https://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-1.jpg)
Equations of Parallel and Perpendicular Lines ALGEBRA 1 UNIT 5: WRITING EQUATIONS OF LINES
![Parallel Lines Parallel Lines](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-2.jpg)
Parallel Lines
![What are parallel lines? Parallel lines are two lines that never intersect each other. What are parallel lines? Parallel lines are two lines that never intersect each other.](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-3.jpg)
What are parallel lines? Parallel lines are two lines that never intersect each other.
![Where have you seen examples in real-life? Lines on a road Lines between bricks Where have you seen examples in real-life? Lines on a road Lines between bricks](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-4.jpg)
Where have you seen examples in real-life? Lines on a road Lines between bricks Floor and ceiling Brainstorm as many examples of parallel lines as possible.
![What characteristics do parallel lines have? Parallel lines are two lines that never intersect What characteristics do parallel lines have? Parallel lines are two lines that never intersect](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-5.jpg)
What characteristics do parallel lines have? Parallel lines are two lines that never intersect each other, BUT: What are their features on a graph? They have the same slope They can have different y- intercepts They still will never intersect
![Parallel Lines Parallel Lines](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-6.jpg)
Parallel Lines
![Determine if lines are parallel or perpendicular 1. Put the equation into slopeintercept form Determine if lines are parallel or perpendicular 1. Put the equation into slopeintercept form](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-7.jpg)
Determine if lines are parallel or perpendicular 1. Put the equation into slopeintercept form ( y = mx +b) 2. Determine if the slopes are the same (parallel) or opposite reciprocals (perpendicular) or neither.
![Determine if the lines are parallel Y = 4 x + 16 Y = Determine if the lines are parallel Y = 4 x + 16 Y =](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-8.jpg)
Determine if the lines are parallel Y = 4 x + 16 Y = 3 x + 1 Y = -4 x – 1 Y = -1/4 x – 4 Y = 4 x - 2
![Determine if two lines are parallel 2 x + 4 y = 10 9 Determine if two lines are parallel 2 x + 4 y = 10 9](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-9.jpg)
Determine if two lines are parallel 2 x + 4 y = 10 9 x + 4 y = 12 Y = -9/4 x – 5 2 y = 18/4 x + 8 Y = - 3 x – 1
![Writing equations of parallel lines I want a line parallel to y = 4 Writing equations of parallel lines I want a line parallel to y = 4](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-10.jpg)
Writing equations of parallel lines I want a line parallel to y = 4 x + 10 that goes through the point (6, 12). How would I do this graphically?
![Writing equations of parallel lines I want a line parallel to y = 4 Writing equations of parallel lines I want a line parallel to y = 4](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-11.jpg)
Writing equations of parallel lines I want a line parallel to y = 4 x + 10 that goes through the point (6, 12). How would I do this algebraically?
![Example I want a line parallel to y = -2 x – 1 and Example I want a line parallel to y = -2 x – 1 and](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-12.jpg)
Example I want a line parallel to y = -2 x – 1 and through the point (3, 6).
![Example I want a line parallel to y = 6 x + 12 and Example I want a line parallel to y = 6 x + 12 and](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-13.jpg)
Example I want a line parallel to y = 6 x + 12 and through the point (0, -10).
![Real- Life Example I am creating a city which is to have two parallel Real- Life Example I am creating a city which is to have two parallel](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-14.jpg)
Real- Life Example I am creating a city which is to have two parallel streets. If I plot the first street such that the equation is y = 2 x – 2 and I want the other street to be 6 units away, what would be the equation of this street?
![Real-Life Example Real-Life Example](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-15.jpg)
Real-Life Example
![Questions? Questions?](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-16.jpg)
Questions?
![Perpendicular Lines Perpendicular Lines](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-17.jpg)
Perpendicular Lines
![What are perpendicular lines? Perpendicular lines are two lines that intersect to form a What are perpendicular lines? Perpendicular lines are two lines that intersect to form a](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-18.jpg)
What are perpendicular lines? Perpendicular lines are two lines that intersect to form a right angle. A right angle is an angle whose measure is 90 degrees.
![Where have you seen examples in real-life? Floor and wall Intersection of two roads Where have you seen examples in real-life? Floor and wall Intersection of two roads](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-19.jpg)
Where have you seen examples in real-life? Floor and wall Intersection of two roads Tiles on the ground Brainstorm as many examples of parallel lines as possible.
![What characteristics do perpendicular lines have? Perpendicular lines are two lines that intersect to What characteristics do perpendicular lines have? Perpendicular lines are two lines that intersect to](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-20.jpg)
What characteristics do perpendicular lines have? Perpendicular lines are two lines that intersect to form a right angle, BUT: What are their features on a graph? They have opposite reciprocal slopes WHY? They can have different y- intercepts
![Perpendicular Lines Perpendicular Lines](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-21.jpg)
Perpendicular Lines
![Determine if two lines are perpendicular x - 3 y = 10 9 x Determine if two lines are perpendicular x - 3 y = 10 9 x](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-22.jpg)
Determine if two lines are perpendicular x - 3 y = 10 9 x + 4 y = 12 Y = -9/4 x – 5 2 y = 18/4 x + 8 Y = - 3 x – 1
![Write equations of perpendicular lines. I want a line perpendicular to y = 4 Write equations of perpendicular lines. I want a line perpendicular to y = 4](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-23.jpg)
Write equations of perpendicular lines. I want a line perpendicular to y = 4 x + 10 that goes through the point (6, 12). How would I do this graphically?
![Write equations of perpendicular lines. I want a line perpendicular to y = 4 Write equations of perpendicular lines. I want a line perpendicular to y = 4](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-24.jpg)
Write equations of perpendicular lines. I want a line perpendicular to y = 4 x + 10 that goes through the point (6, 12). How would I do this algebraically?
![Example I want a line perpendicular to = -2 x – 1 and through Example I want a line perpendicular to = -2 x – 1 and through](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-25.jpg)
Example I want a line perpendicular to = -2 x – 1 and through the point 6). y (3,
![Example I want a line parallel to y = 6 x + 12 and Example I want a line parallel to y = 6 x + 12 and](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-26.jpg)
Example I want a line parallel to y = 6 x + 12 and through the point (0, -10).
![Real- Life Example I am designing an intersection. I need the two streets to Real- Life Example I am designing an intersection. I need the two streets to](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-27.jpg)
Real- Life Example I am designing an intersection. I need the two streets to create a 90 degree angle. If the first street is located on the line y = 4 x – 2 where would I need to build the new road to create this intersection such that the road goes through a town located at a point (4, 7)?
![Real- Life Example Real- Life Example](http://slidetodoc.com/presentation_image/5dc923049fe2bcdec848cb07ffd2392a/image-28.jpg)
Real- Life Example
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