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Zero Slope: Definition & Examples

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  • 0:01 Definition of a Zero Slope
  • 0:12 Zero Slope and Bicycle Rides
  • 2:27 Zero Slope and Graphing
  • 3:15 Lesson Summary
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Lesson Transcript
Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

If the slope of a line is zero, then y does not increase, no matter how much x increases. In this lesson you will learn about lines with zero slope and how that affects a line's equation and graph.

Definition of a Zero Slope

A line with zero slope is perfectly flat in the horizontal direction. No matter what value of x you have, you get the same y-value. It does not increase or decrease.

Zero Slope and Bicycle Rides

Most of the time, we think of slope as 'rise over run', or how much y changes when x changes some amount. For example, suppose you are riding your bicycle along a straight path. You start at the seashore and take a break for lunch at a point 10 miles away. At this lunch stop, you are .25 miles above sea level. To see how steep your climb was, you calculate slope, or rise over run, like this:

Slope = .25/10 = 1/40

Be very careful that you put the rise, which is a vertical climb, on the top of the fraction.

It is perfectly fine to write 1/40 as the equivalent decimal, 0.025, but it isn't essential. Slopes are often written as functions because they make intuitive sense. For example, a slope of 1/40 means you ascend 1 unit vertically for every 40 units you traveled horizontally. 'Units' could be feet, meters, or miles. It doesn't really matter if your bike ride was along a perfectly straight, consistently ascending path.

Now, a slope of 1/40 sounds pretty small, but on a bicycle for 10 miles your legs would probably feel it. If you want a really relaxing ride, then what you want is a slope even smaller than 1/40. Without actually riding downhill, the easiest ride would obviously be on a perfectly flat road. So, what you want is to rise 0 miles (or 0 feet, or 0 meters) no matter how far you ride.

In other words, when you calculate slope, rise over run, you want 0 to be in the numerator (the top of the fraction). It really doesn't matter at all what is on the bottom. No matter how far you ride, your ride will be flat.

For example, your slope might look like this:

Slope = 0/10

OR

Slope = 0/1000

OR

Slope = 0/(0.27)

In each case, when you simplify the fraction, you get 'Slope = 0'. No slope at all. Nada. You rise not one inch no matter how far you ride your bike. Even your Mom could keep up if you pedal nice and slowly.

The important thing to notice is that zero slope means perfectly horizontal.

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