Section 2.1 The Rectangular Coordinate System

Objective 1: Plot ordered pairs on a rectangular coordinate system. 2.1 Lecture Guide: The Rectangular Coordinate System

1.Identify and label: (a) x-axis (b) y-axis (c) origin (d) Quadrants

2. Note that an ordered pair consists of two ___________, an __________________ and a _________________. The one that is always listed first is the _______________.

3. Use the graph in question 1 to fill in each blank. (a) Moving up or down on the coordinate plane changes the ___-coordinate but not the ___-coordinate. (b) Moving left or right on the coordinate plane changes the ___-coordinate but not the ___-coordinate. (c) Every point on the x-axis has a y-coordinate of ______ and every point on the y-axis has an x-coordinate of ______.

4. Identify the coordinates of the point in (a) A (b) B (c) C (d) D A C D B

5. Identify the coordinates of one point that would lie between Quadrants II and I. 6. Identify the coordinates of one point that would lie between Quadrants IV and I.

7. Plot and label the points whose coordinates are given on the following coordinate system. (a) A(– 2, 4) (b) B(5, – 3) (c) C(– 3, – 4 ) (d) D(– 2,0) (e) E(0,3)

Objective 2: Draw a scatter diagram of a set of points. A scatter diagram for a set of data points is simply a graph of these points. 8. Draw a scatter diagram for the following set of points: Do these points lie on a straight line?

Objective 3: Identify data whose graph forms a linear pattern. Arithmetic Sequences: Numerically: An arithmetic sequence has a ________ change, d, from term to term. Graphically: The distinct points of the graph of an arithmetic sequence ______________ pattern. There is a _____________ change in height between consecutive points.

9. Rewrite the sequence using subscript notation.

10. When creating a graph of a sequence, use n as your _________-value and use _________ as your y-value.

11. Represent the following sequence using subscript notation and ordered pair notation. Then complete the table and the graph. Subscript notation: TableGraph Sequence: 3, – 1, – 5, – 9, – 13 nanan Ordered Pair Notation:

12. Consider the given graph of the sequence. (a)Write the first five terms of this sequence. (b) Is this sequence arithmetic? (c) If this sequence is arithmetic, determine the common difference d of this sequence.

13. Consider the given graph of the sequence. (a) Write the first five terms of this sequence. (b) Is this sequence arithmetic? (c) If this sequence is arithmetic, determine the common difference d of this sequence.

14. It is important to observe that the graph of an arithmetic sequence forms a ________________ pattern.

Determine whether each sequence is an arithmetic sequence and whether its graph forms a linear pattern , 8, 12, 16, , 8, 16, 32, 64

17. The equation gives the total payments in dollars after n months on a loan for a new truck. Calculate and interpret each value of. (a) (b) (c)

18. The graph shown below gives the altitude of a small airplane at a given time. The time x is given in minutes from the start of the flight and the altitude y is given in thousands of feet. Answer each question by examining this graph. Altitude in thousands of feet Minutes (a) What was the highest altitude reached by the plane? (b) How long after the flight began did the plane reach this highest altitude? Objective 4: Interpret a line graph.

18. The graph shown below gives the altitude of a small airplane at a given time. The time x is given in minutes from the start of the flight and the altitude y is given in thousands of feet. Answer each question by examining this graph. Altitude in thousands of feet Minutes (c) During what time was the plane flying level? (d) How long was the flight?