My Math Forum Why is undefined slope a vertical line?

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 July 3rd, 2017, 08:37 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, 08:44 PM #2 Senior Member   Joined: Aug 2012 Posts: 1,679 Thanks: 436 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 x-axis 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, 09:38 PM #3 Newbie   Joined: Jun 2017 From: Wisconsin Posts: 15 Thanks: 0 Thank you so much! This helped a ton.
July 4th, 2017, 12:36 AM   #4
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Quote:
 Originally Posted by geekchick Why is this . . .
What did you mean by "this"? You could draw a line between the two points, but it doesn't follow that the line should be part of your graph.

 July 4th, 2017, 10:22 AM #5 Senior Member     Joined: Nov 2015 From: United States of America Posts: 165 Thanks: 21 Math Focus: Calculus and Physics 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 y-axis. While it "runs" 0 units on the x-axis. 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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