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A number line is a visual representation where each point corresponds to a number. It's like a ruler where you can line up numbers, starting from zero in the middle and moving outwards. On one side, you have positive numbers, and on the other side, negative numbers. For instance, you start at zero, then you can go to 1, 2, 3, and so on, to the right. To the left, you go to -1, -2, -3, etc.
One of the key uses of a number line is to illustrate the concept of absolute value. Imagine standing at any point. The absolute value is simply how far you are from zero, no matter if you are to the left or right. This distance is always counted positively.
Therefore, the number line helps make sense of why the absolute value makes a negative number positive, emphasizing distance and position rather than sign.

The absolute value of a number focuses on its distance from zero on the number line. This distance tells us how far a number is from zero, and crucially, this measure is always positive. The reasoning is that distance, as a concept, cannot be negative. You can't have a negative amount of 'space' between two points.
To understand this, imagine you are standing on a number line at -12. To find the distance from zero, you simply count the steps back to zero: there are 12 steps. Importantly, you don't care about the direction of travel, just the number of steps.

• Absolute value of -12 is 12
• The concept ensures the result is always non-negative
• Regardless of direction on the number line, distance is positive

Understanding "distance from zero" in terms of absolute value helps clarify why the negative sign disappears when taking the absolute value of a negative number.

When we talk about positive numbers, these are simply numbers greater than zero. On the number line, they are positioned to the right of zero. These numbers, like 1, 2, 3, and so on, depict "increases" or amounts that are above zero.
In the context of absolute value, recognizing positive numbers is helpful because absolute values are always positive. When finding an absolute value, you are essentially asking, "How far is this number from zero?" Therefore, if a number is already positive, its absolute value is the number itself. No conversion is needed.
Absolute value acts as a sort of "positive converter." For instance, even though -12 is negative, its distance from zero, or absolute value, is 12—a positive number.