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Section 2.1
The Rectangular Coordinate System and Arithmetic Sequences
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Objective: Plot ordered pairs on a rectangular coordinate system.
2.1 Lecture Guide: The Rectangular Coordinate System and Arithmetic Sequences
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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
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2. Note that an ordered pair consists of two __________________, an _____________________ and a _____________________.
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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 ______.
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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
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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.
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7. Plot all points:
(a) with an x-coordinate of 2
-5
5
-5 5
y
x
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7. Plot all points:
(b) with an y-coordinate of 2
-5
5
-5 5
y
x
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7. Plot all points:
(c) with equal x- and y-coordinates
-5
5
-5 5
y
x
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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?
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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.
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9. Rewrite the sequence 5, 1, 3, 7, 11 using subscript notation.
1 ______a
2 ______a
3 ______a
4 ______a
5 ______a
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10. When creating a graph of a sequence, use n as your ______-value and use ______ as your output-value.
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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
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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
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13. It is important to observe that the graph of an arithmetic sequence forms a ________________ pattern.
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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.
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15. Determine the first 5 terms of the arithmetic sequence given that 1 6a and 2d
1 2 3 4 5
n
n
a
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16. Determine the first 5 terms of the arithmetic sequence given that 10 32na n
1 2 3 4 5
n
n
a
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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
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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?
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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?