Using Vertical and Horizontal Number Lines to Represent Integers
The GED Mathematical Reasoning test uses both horizontal and vertical number lines to represent integers in different real-world contexts. A horizontal number line models situations like temperature along a timeline, while a vertical number line models situations like elevation above and below sea level. Mastering both orientations is an essential GED Math skill.
What Are Vertical and Horizontal Number Lines?
Both number lines represent the same set of integers, just oriented differently. A horizontal number line runs left to right, with positive integers to the right of zero and negative integers to the left. A vertical number line runs up and down, with positive integers above zero and negative integers below zero. The key insight is that direction and value are linked: right/up means greater; left/down means lesser.
Reading and Plotting Integers on Both Orientations
Horizontal number line
Positive integers are to the right of zero; negative integers are to the left. Moving right increases value; moving left decreases it.
- \(\color{blue}{3}\) is 3 units right of zero.
- \(\color{blue}{-5}\) is 5 units left of zero.
Vertical number line
Positive integers are above zero; negative integers are below zero. Moving up increases value; moving down decreases it.
- \(\color{blue}{4}\) is 4 units above zero.
- \(\color{blue}{-3}\) is 3 units below zero.
Real-world connections
- Horizontal: a timeline (years BCE and CE), temperatures along a day.
- Vertical: altitude above/below sea level, floors above/below ground in a building.
Step-by-Step Summary
- Identify whether the number line is horizontal or vertical.
- Locate zero as the center reference point.
- For positive integers: move right (horizontal) or up (vertical).
- For negative integers: move left (horizontal) or down (vertical).
- Count tick marks equal to the absolute value of the integer.
- Mark and label the point.
Watch: Integers on Horizontal & Vertical Number Lines (Video Lesson)
This lesson shows how to plot integers on both types of number lines side by side:
Worked Examples
Example 1: Plot \(\color{blue}{-3}\) on a horizontal number line.
Start at zero. Move 3 units to the left. Mark the point and label it \(\color{blue}{-3}\).
Example 2: A submarine is 40 meters below sea level. Represent this on a vertical number line.
Sea level = \(\color{blue}{0}\). Below sea level is negative. Move 40 units below zero and mark the point \(\color{blue}{-40}\).
Example 3: On a vertical number line representing elevation, point A is at \(\color{blue}{-15}\) feet and point B is at \(\color{blue}{20}\) feet. Which is higher? What is the distance between them?
Point B (\(\color{blue}{20}\)) is above zero; point A (\(\color{blue}{-15}\)) is below zero. B is higher.
Distance: \(\color{blue}{20 – (-15) = 20 + 15 = 35}\) feet.
Example 4: On a horizontal number line, plot the integers \(\color{blue}{-4, -1, 2, 5}\) and compare \(\color{blue}{-4}\) and \(\color{blue}{-1}\).
Plotting: \(\color{blue}{-4}\) is 4 left, \(\color{blue}{-1}\) is 1 left, \(\color{blue}{2}\) is 2 right, \(\color{blue}{5}\) is 5 right.
Since \(\color{blue}{-1}\) is to the right of \(\color{blue}{-4}\), we have \(\color{blue}{-1 > -4}\).
More Practice: Graphing Integers on Both Number Lines (Video)
This video provides additional graphing practice on horizontal and vertical number lines:
Exercises
- On a horizontal number line, plot \(\color{blue}{-6}\), \(\color{blue}{-2}\), \(\color{blue}{1}\), and \(\color{blue}{4}\).
- On a vertical number line, a fish is at \(\color{blue}{-8}\) meters and a bird is at \(\color{blue}{12}\) meters. What is the distance between them?
- Which is farther from zero: \(\color{blue}{-9}\) or \(\color{blue}{7}\)? On which type of number line is this easiest to see?
- A building has floors labeled \(\color{blue}{-2}\) (basement), \(\color{blue}{0}\) (ground), and \(\color{blue}{5}\) (top). Plot these on a vertical number line.
- On a horizontal number line, which integer is 4 units to the left of \(\color{blue}{1}\)?
- Compare \(\color{blue}{-7}\) and \(\color{blue}{-2}\) using a number line. Write the correct inequality.
Answers
- From left to right: \(\color{blue}{-6, -2, 1, 4}\).
- \(\color{blue}{12 – (-8) = 20}\) meters.
- \(\color{blue}{-9}\) is farther from zero (absolute value 9 vs. 7); a vertical number line makes distances from zero visually clear.
- From bottom: \(\color{blue}{-2}\), then \(\color{blue}{0}\), then \(\color{blue}{5}\) at top.
- \(\color{blue}{1 – 4 = -3}\).
- \(\color{blue}{-2 > -7}\) (since \(\color{blue}{-2}\) is to the right/above \(\color{blue}{-7}\)).
Frequently Asked Questions
What is the difference between a horizontal and a vertical number line?
They represent the same integers in different orientations. Horizontal lines run left-right (positive right, negative left). Vertical lines run up-down (positive up, negative down). The rules for comparison and plotting are identical; only the direction changes.
When does the GED use a vertical number line?
Vertical number lines appear in contexts involving elevation (above/below sea level), temperature (above/below freezing), or floors in a building. Recognizing the orientation helps you interpret real-world problems correctly.
How do I remember which direction is positive?
Think of a thermometer (vertical): temperature rises upward, so positive is up. Think of a timeline (horizontal): future dates go right, so positive is right. Both orientations follow the same “\(\color{blue}{\text{ greater } = \text{ further }}\) in the positive direction” rule.
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