Slope Specials

Scott Solomon

Vertical, Horizontal, Parallel, Perpendicular


Slope of a Vertical Line
Undefined
x = 3
vertical


Slope of a Horizontal Line
Zero
y = 3
horizontal


Slope of Parallel Lines
Equal (parallel lines never cross each other)
Because m = 2 for both lines,  y = 2x + 2 is parallel to y = 2x + 5
parallel


Slope of Perpendicular Lines
Negative Inverse (perpendicular lines cross at a right angle to each other)
Because 2 and –\bf\displaystyle\frac{1}{2} are negative inverses, y = 2x + 2 is perpendicular to y = –\bf\displaystyle\frac{1}{2} x + 4
perpendicular


Question
What is the slope of x = 7

Answer
Undefined


Question
What is the slope of y = 8

Answer
0


Question
The equations of two lines are y = -9x +4 and y = -9x +7, respectively.
True or False: Are these lines parallel?

Answer
True

Answer Process
Because the slopes of the two lines are the same, -9, the lines are parallel.


Question
The equations of two lines are y = –\bf\displaystyle\frac{1}{8} x + 4 and y = 8x – 3, respectively.
True or False: Are these lines perpendicular?

Answer
True

Answer Process
Because the slopes of the two lines are negative inverses, –\bf\displaystyle\frac{1}{8} and 8, the lines are perpendicular.


Practice – Questions
1.  What is the slope of x = -7?

2.  What is the slope of y = -3?

3.  The equations of two lines are y = 7x + 5 and y = 7x – 3, respectively.
True or False: Are these lines parallel?

4.  The equations of two lines are y = –\bf\displaystyle\frac{1}{3} x + 9 and y = 3x – 6, respectively.
True or False: Are these lines perpendicular?

5.  The equations of two lines are y = \bf\displaystyle\frac{1}{5} x + 2 and y = -5x – 4, respectively.
True or False: Are these lines perpendicular?


Practice – Answers
1.  Undefined

2.  0

3.  True

4.  True

5.  True

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