1. Algebra 1
Section 1.2

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

3. 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

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

5. 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

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

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

8. 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

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

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

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

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

13. Homework: pp