Using an example, explain how absolute value can be used to represent the distance between two values on a number line.
d = | b-a|
since a-b = -(b-a)
then
d = |a-b| = |b-a|
To understand how absolute value can represent the distance between two values on a number line, let's consider an example. Suppose we have two numbers, -5 and 3, and we want to find the distance between them using the absolute value.
Step 1: Identify the two numbers on the number line. In our example, -5 is to the left of the origin (0) and 3 is to the right of the origin.
Step 2: Calculate the difference between the two numbers. To find the difference, we subtract the smaller number from the larger number. In our example, we have 3 - (-5), which simplifies to 3 + 5 = 8.
Step 3: Take the absolute value of the difference. The absolute value of a number is its distance from zero on the number line. In our example, the absolute value of 8 is simply 8. This represents the distance between -5 and 3 on the number line.
To summarize, to find the distance between two values on a number line using absolute value, subtract the smaller value from the larger value, and then take the absolute value of the difference.