Section 2.1

The Rectangular Coordinate System and Arithmetic Sequences

Objective: Plot ordered pairs on a rectangular coordinate system.

2.1 Lecture Guide: The Rectangular Coordinate System and Arithmetic Sequences

1. Identify and label:

2, 4

5, 3

(a) x-axis

(b) y-axis

(c) origin

(d) Quadrants

(e)

(f) -5

5

-5 5

(g)

(h)

2, 0

0, 3

2. Note that an ordered pair consists of two __________________, an _____________________ and a _____________________.

3. Use the graph in question 1 to fill in each blank. See Calculator Perspective 2.1.1 to explore these questions with your calculator.

(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) Quadrant II

(b) Quadrant IV

(c) Quadrant III

(d) Quadrant I

-5

5

-5 5

y

x

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 all points:

(a) with an x-coordinate of 2

-5

5

-5 5

y

x

7. Plot all points:

(b) with an y-coordinate of 2

-5

5

-5 5

y

x

7. Plot all points:

(c) with equal x- and y-coordinates

-5

5

-5 5

y

x

Objective: 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:

6 3 0 3 6

6 4 2 0 2

x

y

-6

6

-6 6

y

x

Do these points lie on a straight line?

Objective: Identify an arithmetic sequence.

Arithmetic Sequences:

Numerically: An arithmetic sequence has a constant change, d, from term to term.

Graphically: The distinct points of the graph of an arithmetic sequence all lie on a straight line. There is a constant change in height between consecutive points.

9. Rewrite the sequence 5, 1, 3, 7, 11 using subscript notation.

1 ______a

2 ______a

3 ______a

4 ______a

5 ______a

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

11. Complete the table and the graph and determine whether the sequence is arithmetic.

Sequence 3, 1, 5, 9, 13

Table

1

2

3

4

5

x y

Graph

-14

4

-1 6

y

x

Arithmetic Yes / No

12. Complete the table and the graph and determine whether the sequence is arithmetic.

Sequence Table

1

2

3

4

5

x y

Graph

Arithmetic Yes / No

6, 5, 3, 1, 8

-10

6

-1 6

y

x

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

14. Consider the given graph of the sequence.

-4

8

-1 6

na

n

(a) Is this sequence arithmetic?

(b) Write the first five terms of this sequence.

(c) Determine the common difference d of this sequence.

15. Determine the first 5 terms of the arithmetic sequence given that 1 6a and 2d

1 2 3 4 5

n

n

a

16. Determine the first 5 terms of the arithmetic sequence given that 10 32na n

1 2 3 4 5

n

n

a

17. The equation 300 1000na n gives the total paymentsin dollars after n months on a loan for a new truck. Calculate and interpret each value of na . (a)

(b)

(c)

0a

12a

24a

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.

0

1

2

3

4

5

0 10 20 30 40 50 60 70

y

x

Alt

itu

de

in

tho

usa

nd

s o

f fe

et

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?

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.

0

1

2

3

4

5

0 10 20 30 40 50 60 70

y

x

Alt

itu

de

in

tho

usa

nd

s o

f fe

et

Minutes

(c) During what time was the plane flying level?

(d) How long was the flight?