# why does a vertical line have no slope

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is called the slope of the line, and is the y-coordinate where the line crosses the y-axis. If it has a slope 0, this would give, so a horizontal line. Alternatively, every horizontal line has the form, so a slope 0. , which can't be written as and has therefore no slope. However, you can apporximate a vertical line by taking a very steep line. For instance, if we take the ine, we can approximate it by taking can be either negative or positive). So if you would make larger and larger, you would approximate the line to a better and better degree.

So in some sense you could say that by taking the limit of, you would get the vertical line. Date: 04/11/97 at 12:31:39 From: Shelia V. Atkins Subject: Undefined Slope and Zero Slope What is the difference between an undefined slope and a slope of zero? I have read my book, and I can't seem to find the answer anywhere. Date: 04/11/97 at 13:59:34 From: Doctor Mike Subject: Re: Undefined Slope and Zero Slope Dear Shelia, Yes, this is a subtle difference.

Here is the straight info. A horizontal line has a slope which is the number zero. You might be familiar with the standard "slope/intercept" form of the equation of a line y = mx+b where m stands for the slope. If you use zero for m you just get y = b which is the standard form for a horizontal line. A vertical line does not have a slope. It's not a question of not knowing what the slope is equal to; it doesn't exist.

There isn't one. That is what is meant by saying it has "undefined" slope. Here's another way to look at it. If you take a horizontal line and tilt it more and more so it gets closer and closer to being vertical (straight up and down) but not actually vertical, then the slope of the line gets bigger and bigger. If a line is just one degree away from being vertical then its slope is about 57. If a line is only 1/10 of a degree away from being vertical, then its slope is about 573.

You could even have a line which is *almost* vertical with a slope of one billion! Following this trend, the slope of a vertical line would have to be infinity, but infinity is not a real number, so we just have to say that the idea of slope is not defined or doesn't make sense for a vertical line. I hope this helps. -Doctor Mike, The Math Forum Check out our web site! http://mathforum. org/dr. math/

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