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GMAT Prep: Tutoring Solution23 chapters | 223 lessons

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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.

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.

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.

When you are graphing lines in mathematics classes, you may also encounter a horizontal line. Just like in the bicycling example, a horizontal line goes with zero slope. One thing to be aware of when you graph, however, is that this horizontal line can be any *height*. For example, the picture you see here has three horizontal lines. In each case the slope is zero.

You might also notice the equations of the lines on the left hand side of the picture. They are all similar, and they all look like 'y = something.'

Most of the time, an equation of a line has an *x* and a *y* in it. When the slope of the line is zero, however, the number that is right in front of the *x* is zero. That makes the *x* drop out of the equation altogether. So, you end up with an equation that looks like: *y*= 4.

The slope of a line can be thought of as 'rise over run.' When the 'rise' is zero, then the line is horizontal, or flat, and the slope of the line is zero. Put simply, a **zero slope** is perfectly flat in the horizontal direction. The equation of a line with zero slope will not have an *x* in it. It will look like 'y = something.'

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GMAT Prep: Tutoring Solution23 chapters | 223 lessons

- Graph Functions by Plotting Points 8:04
- Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative 5:49
- Linear Equations: Intercepts, Standard Form and Graphing 6:38
- How to Find and Apply The Slope of a Line 9:27
- How to Find and Apply the Intercepts of a Line 4:22
- Graphing Undefined Slope, Zero Slope and More 4:23
- Equation of a Line Using Point-Slope Formula 9:27
- How to Use The Distance Formula 5:27
- How to Use The Midpoint Formula 3:33
- What is a Parabola? 4:36
- Parabolas in Standard, Intercept, and Vertex Form 6:15
- How to Graph Cubics, Quartics, Quintics and Beyond 11:14
- Compound Inequality: Definition & Concept
- Negative Slope Lines: Definition & Examples 4:39
- Y-Intercept: Definition & Overview
- Zero Slope: Definition & Examples 3:44
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