Problem 38 - Beginning and Intermediate Algebra

Question

Graph each number on a number line. -5,-3,-2,0,4

Step-by-Step Solution

Answer

Plot -5, -3, -2, 0, and 4 at their respective positions on the number line.

Step 1 - Draw a Number Line

Draw a horizontal line and mark points at equal intervals. This is your number line.

Step 2 - Label the Number Line

Start labeling the points on the number line. Include both negative and positive numbers. Make sure to include at least from -5 to 4, as these encompass all the numbers given.

Step 3 - Locate -5 on the Number Line

Find the location where -5 would be. This is five units to the left of 0. Mark it clearly.

Step 4 - Locate -3 on the Number Line

Find the location where -3 would be. This is three units to the left of 0. Mark it clearly.

Step 5 - Locate -2 on the Number Line

Find the location where -2 would be. This is two units to the left of 0. Mark it clearly.

Step 6 - Locate 0 on the Number Line

Find the location where 0 would be. This is the central point on your number line. Mark it clearly.

Step 7 - Locate 4 on the Number Line

Find the location where 4 would be. This is four units to the right of 0. Mark it clearly.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are located to the left of zero on a number line. For example, in the exercise, numbers like -5, -3, and -2 are negative numbers. Each step to the left on the number line represents a decrement by one unit.
Negative numbers often represent losses or decreases. For instance, -5 could signify a negative change of 5 units from zero.

Positive Numbers

Positive numbers are numbers greater than zero. They are always located to the right of zero on a number line. In the given exercise, 4 is an example of a positive number. Each step to the right on the number line means an increment by one unit.
Positive numbers represent gains or increases. So, 4 means an increase of 4 units from zero.

Number Intervals

Number intervals refer to the range between two numbers on a number line. For example, the interval from -5 to -3 includes the numbers -5, -4, and -3.
Intervals help describe the distance between numbers. When marking intervals on a number line, it is crucial to maintain equal spacing so that each unit is properly represented.
This helps in understanding how far apart numbers are and makes it easier to graph them accurately.

Zero on Number Line

Zero is a central point on a number line. It separates positive numbers from negative numbers. Zero is neither positive nor negative and serves as a starting point for counting in both directions.
In the exercise, zero is the middle point. All negative numbers like -5, -3, and -2 are to the left of zero, while positive numbers like 4 are to the right.
Placing zero accurately is key to ensuring other numbers are correctly graphed. It’s like the anchor point for your number line.