Problem 35 - Beginning and Intermediate Algebra

Question

Graph each number on a number line. 0,3,-5,-6

Step-by-Step Solution

Answer

Plot points at 0, 3, -5, and -6 on the number line.

Step 1: Draw a Number Line

Draw a horizontal line and mark the center point as 0. This will be the reference point for placing the other numbers.

Step 2: Mark Positive Numbers

To the right of 0, mark equal intervals for positive numbers. Begin with 1, 2, and continue to 3. Place the number 3 at the third interval to the right of 0.

Step 3: Mark Negative Numbers

To the left of 0, mark equal intervals for negative numbers. Begin with -1, -2, and continue past -3 to -5 and -6. Place the number -5 at the fifth interval to the left of 0 and -6 at the sixth interval.

Step 4: Plot Each Number

Place a point on each number's corresponding position on the number line. Place points at 0, 3, -5, and -6 accordingly.

Key Concepts

number line

A number line is a visual representation of numbers in a straight horizontal line. Each point on the line corresponds to a number, making it easier to understand their relative positions.
To draw a number line, follow these steps:

• Draw a straight horizontal line.
• Mark the center as 0. This is your reference point.
• Mark equal intervals to the right of 0 for positive numbers and to the left of 0 for negative numbers.

By using a number line, you can easily compare numbers, understand their order, and perform basic operations like addition and subtraction.

positive and negative numbers

Numbers can be either positive or negative. Positive numbers are greater than zero and are usually written without a sign (+). Negative numbers are less than zero and always carry a negative sign (-).
In real life, positive numbers can represent things like gains or elevations above sea level, while negative numbers can represent losses or depths below sea level.
On a number line:

• Positive numbers are placed to the right of 0.
• Negative numbers are placed to the left of 0.

For example, 3 is a positive number and is placed three intervals to the right of 0. Conversely, -6 is a negative number and is placed six intervals to the left of 0.

plotting points

Plotting points on a number line involves placing a dot at the position corresponding to a specific number.
Here’s how you can plot points on a number line:

• Identify the position of the number you want to plot.
• Count the intervals to that number from 0, making sure to go right for positive numbers and left for negative numbers.
• Place a dot exactly at that position.

For example, to plot -5 on a number line, count five intervals to the left of 0 and place a dot there. Similarly, to plot 3, count three intervals to the right of 0 and place a dot there.
This method makes it easier to visualize and understand the locations and relationships between different numbers.