Problem 22 - Algebra 1: Concepts and Skills

Question

Graph the numbers on a number line. \(-4,4,-5\)

Step-by-Step Solution

Answer

Numbers -4, -5, and 4 are plotted on the number line. -5 is the furthest to the left, followed by -4, and 4 is on the right of 0.

Step 1: Understanding a number line

A number line is a line, the points of which correspond to numbers. The numbers to the right are positive and those to the left are negative. The central point, known as the origin, represents the number 0.

Step 2: Identify the numbers

Now, let's identify the numbers that have to be plotted on the number line, which include -4, 4, -5.

Step 3: Draw the number line

Draw a straight horizontal line. Mark a point near the middle. This point represents 0. To the right of this point, mark off equal intervals for positive numbers and to the left, do the same for negative numbers.

Step 4: Plotting the numbers

Now, plot each given number on the number line where -4 and -5 are plotted on the left side of 0 (since they are negative) and 4 is plotted on the right side (since it is positive). Make sure the order in each quadrant is as per the numerical values of the numbers.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They help us represent values in situations like debts or temperatures below freezing. These numbers are positioned to the left of zero on a number line. Understanding negative numbers:

• Symbol: Negative numbers are denoted with a minus sign (-), such as -4, -3, and -5.
• Usage: They indicate loss, deficiency, or a decrease in value.

On the number line, -4 and -5 would be placed on the left side of zero, each distance from zero proportional to their value. Remember, the more negative a number is, the farther it is from zero in the negative direction.

Positive Numbers

Positive numbers are greater than zero and can represent quantities, like money earned or heights above sea level. They are found to the right of zero on a number line. Let’s delve deeper:

• Symbol: Positive numbers often have no sign or a plus sign (+), like +4 or simply 4. The plus is usually understood and often not written.
• Usage: Indicates gain, surplus, or increase in quantity.

To represent positive numbers on a number line, you move to the right of zero. For instance, the number 4 would be placed four equal spaces to the right of zero.

Graphing Numbers

Graphing numbers involves visually placing numbers on a number line. It helps us understand the relationships amongst the numbers clearly. Steps to graph numbers:

• Draw the Line: Start by drawing a horizontal line. Place a mark in the center to signify zero, or the origin.
• Mark Intervals: Equidistant points are placed along this line. Positive units to the right of zero and negative units to the left.
• Plot the Numbers: Place the numbers at their corresponding positions on the number line. For example, -5 and -4 would be left, while +4 would be right of zero.

This visual representation simplifies comparisons and arithmetic operations, making it a vital tool in learning mathematics. By graphing, you can easily grasp where different numbers fall in relation to each other.