Algebra 1 Section 1.2

The Number Line The number line extends without limit in both directions Origin: the point at zero Positive numbers are to the right of zero Negative numbers are to the left of zero

The Number Line A point on the number line is called the graph of a number Named with a capital letter The number associated with the point is called a coordinate

The Number Line Numbers increase in value from left to right -3 > -5 2 < 4

The Number Line Number lines can be divided into units of one, or units greater or smaller than one Number lines can be drawn horizontally or vertically

Definition Opposite numbers: numbers that are the same distance from zero but are on opposite sides of zero

Example 3 State the opposite of each number: a. 12 b. -37 c. -4.7 d. -12 37 4.7 -  2  2

Definition The absolute value of a number, denoted |x|, is the number of units (distance) between zero and the number’s graph on a number line

Example 4 Find each absolute value. a. |4| b. |-3| 4 3 Distances are never negative; therefore, absolute values are never negative

Example 5 Simplify. a. |74| – |-24| = 74 – 24 = 50 b. |82 – 31| = |51| = 51

Formula The length, l, of a segment is the absolute value of the difference of the endpoints’ coordinates l = |b – a|

Formula The coordinate of the midpoint, m, of a segment is the average of the endpoints’ coordinates m = a + b 2

Homework: pp. 10-11