Math Assignment Help With Number Lines

Number Lines

15.1 Introduction: A number line is a line in which real numbers can be placed, according to their value. Each point on a number line corresponds to a real number, and each real number has a unique point that corresponds to it. For example, the number 1.5 (1 1/2) corresponds with the point on a number line that is halfway between one and two.

Often the only integers are shown as specially-marked points evenly spaced on the line.

Although in this image only the integers from −9 to 9 are shown, the line includes all numbers. The arrows on both the sides of the line mean that the line continues till infinity i.e. it contains all the real numbers from minus infinite to plus infinite.

The points on a number line are called coordinates. The zero point is called the origin. The numbers to the right of the origin are positive numbers; the numbers to the left of the origin are negative numbers.

15.2 Drawing the number line:

The number line is always represented as a horizontal line. Positive numbers lie on the right side of zero, and negative numbers lie on the left side of zero. An arrowhead is put on either end of the line which is meant to suggest that the line continues indefinitely in the positive and negative directions, as already suggested above.

Characteristics of a number line

1. It is a horizontal line.

2. The points on a number line are called coordinates.

3. The zero point is called the origin.

4. The numbers to the right of the origin are called positive numbers and the numbers to the left of the origin are called negative numbers.

5. It has two arrow heads on either end of the line. This represents that the line extends up to infinity.

15.3 Decimal number line: To represent decimals on number line, divide each segment into 10 parts.

Example: represent 6.5 in the number line.

Draw a number line, dividing the segment between 6 and 7 into 10 equal parts

5.4 Graphing Inequalities on a Number Line

A number line is a horizontal line having points which correspond to numbers. The points are spaced according to the value of the numbers and are equally spaced.

We can graph real numbers by representing them as points on the number line. For example, we can graph 3 ¼ on the number line:

We can also graph inequalities on the number line.

The following graph represents the inequality x≤  3 ¼.

The dark line represents all the numbers that satisfy x≤ 3 ¼.

Take any number on the dark line and plug it in for x, the inequality will be true.

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