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Homework (2/23/2017) Worksheet: Perpendicular, Parallel, or Neither?

Perpendicular and Parallel Lines Students will be able to use slope to determine if two lines are perpendicular, parallel, or neither.

YouTube https://www.youtube.com/watch?v=7eUdRomZyjY https://www.youtube.com/watch?v=ZHmQahVXCps https://www.youtube.com/watch?v=OzJmbcnQ3_Y https://www.youtube.com/watch?v=eDWpM3YOYQI

Parallel lines Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope.

Perpendicular Lines Look at the slope in order to determine if two lines are perpendicular If two lines are negative reciprocal of each other, then they are perpendicular to each other. If one slope is undefined (vertical line) and the other slope is zero (horizontal line), then they are perpendicular.

Negative Reciprocal To find the negative reciprocal, flip the number and then if it's positive make it negative -- and if it's negative make it positive! 3  -3/5  4/7  -1/3 5/3 -7/4

Find the “negative reciprocal” of each fraction

To determine if lines are parallel or perpendicular, you need to change the equation into slope-intercept form (y=mx+b)

Parallel Lines Determine if the lines are parallel 1. 2x + 6y = 12 6y = -2x + 12 yes

Parallel Lines Determine if the lines are parallel 2. 6x + 8y = -24 8y = -6x – 24 No

Parallel Lines Determine if the lines are parallel 3. 4x + 6y = -2 6y = -4x – 2 No

Perpendicular Lines 13. Determine if the lines are perpendicular: and No 14. Determine if the lines are perpendicular: Yes

Testing if Lines are Parallel Are the lines parallel? Find the slope of The slope m = -4 Find the slope of The slope m = -4 Since the slopes are equal the lines are parallel.

Graphs of Parallel Lines The red line is the graph of y = – 4x – 3 and the blue line is the graph of y = – 4x – 7

Practice Testing if Lines are Parallel Are the lines parallel? (click mouse for answer) Since the slopes are different the lines are not parallel. parallel? (click mouse for answer) Are the lines Since the slopes are equal the lines are parallel.

Testing if Lines Are Perpendicular Since the slopes are negative reciprocals of each other the lines are perpendicular.

Graphs of Perpendicular Lines The red line is the graph of y = – 2x + 5 and the blue line is the graph of y = – 1/2 x +4

Practice Testing if Lines Are Perpendicular Since the slopes are not negative reciprocals of each other (their product is not -1) the lines are not perpendicular Since the slopes are negative reciprocals of each other (their product is -1) the lines are perpendicular.