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July 3rd, 2017, 07:37 PM   #1
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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?
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July 3rd, 2017, 07:44 PM   #2
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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.
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July 3rd, 2017, 08:38 PM   #3
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Thank you so much! This helped a ton.
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July 3rd, 2017, 11:36 PM   #4
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Originally Posted by geekchick View Post
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.
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July 4th, 2017, 09:22 AM   #5
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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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