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.

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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

1. Identify whether the number line is horizontal or vertical.
2. Locate zero as the center reference point.
3. For positive integers: move right (horizontal) or up (vertical).
4. For negative integers: move left (horizontal) or down (vertical).
5. Count tick marks equal to the absolute value of the integer.
6. 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

1. On a horizontal number line, plot \(\color{blue}{-6}\), \(\color{blue}{-2}\), \(\color{blue}{1}\), and \(\color{blue}{4}\).
2. 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?
3. Which is farther from zero: \(\color{blue}{-9}\) or \(\color{blue}{7}\)? On which type of number line is this easiest to see?
4. 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.
5. On a horizontal number line, which integer is 4 units to the left of \(\color{blue}{1}\)?
6. Compare \(\color{blue}{-7}\) and \(\color{blue}{-2}\) using a number line. Write the correct inequality.

Answers

1. From left to right: \(\color{blue}{-6, -2, 1, 4}\).
2. \(\color{blue}{12 – (-8) = 20}\) meters.
3. \(\color{blue}{-9}\) is farther from zero (absolute value 9 vs. 7); a vertical number line makes distances from zero visually clear.
4. From bottom: \(\color{blue}{-2}\), then \(\color{blue}{0}\), then \(\color{blue}{5}\) at top.
5. \(\color{blue}{1 – 4 = -3}\).
6. \(\color{blue}{-2 > -7}\) (since \(\color{blue}{-2}\) is to the right/above \(\color{blue}{-7}\)).

Horizontal vs. Vertical Number Lines at a Glance

Both number lines work the same way. Only the direction changes. This table puts them side by side.

The last row is worth remembering. When you graph a point like (3, −4) on the coordinate plane, you are really using both number lines at once: move 3 right on the horizontal one, then 4 down on the vertical one.

Common Mistakes with Negative Numbers on a Number Line

• Thinking −8 is bigger than −3. The digit 8 is larger, but −8 is farther from zero in the negative direction. On a vertical line, −8 is lower, so −8 < −3.
• Uneven spacing. Each step must be the same size. If one mark is 1 unit, every mark is 1 unit.
• Counting the starting mark. To plot −4, start at 0 and take 4 jumps down or left. Do not count 0 as a jump.
• Forgetting fractions and decimals. Numbers like −1.5 or −2½ go between the integer marks. −1.5 sits halfway between −1 and −2.

Frequently Asked Questions

What is a vertical number line?

A vertical number line runs up and down instead of left to right. Zero sits in the middle, positive integers go above it and negative integers go below it, so numbers get larger as you move up. Thermometers and elevation charts work this way, which makes vertical number lines handy for problems about temperature or depth below sea level.

How do you show negative numbers on a vertical number line?

Mark zero, draw equally spaced ticks above and below it, and place negative numbers below zero. To plot −4, start at zero and count 4 ticks down. A submarine at 30 feet below sea level would be plotted at −30 on a vertical line scaled by tens, three marks under the zero line that stands for sea level.

What is a horizontal number line?

A horizontal number line is a straight line drawn from left to right with zero near the center. Positive integers lie to the right of zero and negative integers lie to the left, so values increase as you move right. For example, 3 sits three units right of zero, while −3 sits the same distance to the left.

What is the vertical number line called?

On the coordinate plane, the vertical number line is called the y-axis, and the horizontal number line is called the x-axis. The two lines cross at zero on both, a point called the origin, written (0, 0). To plot (3, −2), move 3 units right along the x-axis, then 2 units down parallel to the y-axis.

Which number line plots the integers −6, −2, and 5?

The correct number line shows −6 farthest left (or lowest on a vertical line), −2 between −6 and zero, and 5 on the positive side. Check the distances from zero: −6 is 6 units away, −2 is 2 units away and 5 is 5 units away. In order from least to greatest, the integers are −6, −2, 5.

How do you plot integers on a number line?

Start at zero, then count units in the direction that matches the sign. Positive integers go right on a horizontal line or up on a vertical line, and negative integers go left or down. To plot −7 and 2, count 7 units left of zero for −7 and 2 units right for 2, then mark each point with a dot.

Related Topics

• Using Number Lines to Represent Integers
• Opposite Integers
• Integers and Absolute Value
• Compare the Temperatures Above and Below Zero
• Adding and Subtracting Integers