Final answer:
To graph a set of numbers on a number line, select opening and closing numbers that encapsulate the smallest and largest values of the set. Then, choose a scalable increment that allows for precise placement of both whole numbers and decimals, ensuring a uniform scale across the line.
Step-by-step explanation:
To graph the numbers -4, 2.5, -0.6, -5, √2, 3, 3, and 4.74 on a number line, you need to select suitable opening and closing numbers for the calibrations of the number line. The opening number should be lower than the smallest number in the set, and the closing number should be higher than the largest number in the set. Considering the given numbers, the smallest is -5 and the largest is an approximation for √2 (which is about 1.4142) and then 4.74. Therefore, you might start your number line at -6 and end it at 5, to ensure all numbers can be comfortably placed.
Following that, you'll want to decide on the increments to use on the number line. Since the numbers include decimal places, it might be prudent to use increments of 0.5 or 1 on the number line. This will allow you to place both whole numbers and decimals accurately. Once the scale is set, mark each number on the line at the appropriate point with a dot or a vertical tick. For instance, -4 would be four units to the left of 0, 2.5 would be two and a half units to the right, and so forth. The square root of 2, which is an irrational number, would be placed a little more than 1.4 units to the right of 0.
Remember to keep the scale uniform across the number line to accurately represent the differences between the numbers. Once all the numbers are plotted, you'll have a visual representation of their positions in relation to one another.