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July 3rd, 2017, 07:37 PM  #1 
Newbie Joined: Jun 2017 From: Wisconsin Posts: 15 Thanks: 0  Why is undefined slope a vertical line?
Let's say I have two points: (2,4) and (2,3). The slope would be 7/0 which is undefined. Why is this a vertical line and where on the graph would it fall?

July 3rd, 2017, 07:44 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,510 Thanks: 364 
Any two points determine a line. Since both points have the same x coordinate the line through them is vertical. Another way to look at it is that as the angle between the line and the positive xaxis goes from zero to $\frac{\pi}{2}$, the slope goes from zero to infinity. It's helpful to look at some examples and draw pictures. 
July 3rd, 2017, 08:38 PM  #3 
Newbie Joined: Jun 2017 From: Wisconsin Posts: 15 Thanks: 0 
Thank you so much! This helped a ton.

July 3rd, 2017, 11:36 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,903 Thanks: 1381  
July 4th, 2017, 09:22 AM  #5 
Senior Member Joined: Nov 2015 From: Alabama Posts: 140 Thanks: 17 Math Focus: Geometry, Trigonometry, Calculus 
Another way to visualize this slope of 7/0 is to think about rise over run (rise/run). The line "rises" 7 units on the yaxis. While it "runs" 0 units on the xaxis. So the line defined by those two points will always be "rising" and never "running", therefore being a vertical line in the coordinate plane. You can graphically visualize this by making a line between the points (2,4) and (2,3). It would be a vertical line 7 units long lying on x=2. 

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line, slope, undefined, vertical 
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