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
6.6
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.
<
3.5
Graph of x > 2
2
The circle on the graph shows that 2 is not the solution to x>2
Graph x≠ 2
2
The graph shows
that all the real values are the solution for x except the point having the open circle