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Analyze patterns and relationships
Overview
See “Graphing Points on a Coordinate Plane” before completing this section.
We can use what we know about patterns to complete the chart below.
| Point | x Rule: Add 2 |
y Rule: Add 4 |
Ordered Pair (x, y) |
| A | 2 | 4 | (2, 4) |
| B | |||
| C | |||
| D |
For the x-coordinates, we add 2 to each row.
For the y-coordinate, we add 4 to each row.
We list the ordered pairs using a set of parenthesis. Always list the x-coordinate first, then the y-coordinate.
Graphing the Results
Once we’ve determine the ordered pairs, we can create a visual by plotting the
points on a coordinate plane.
| x Rule: Add 2 |
y Rule: Add 4 |
Ordered Pair (x, y) |
| 2 | 4 | (2, 4) |
| 4 | 8 | (4, 8) |
| 6 | 12 | (6, 12) |
Remember
Travel across the x-axis first.
Then travel up the y-axis.
Use a ruler to connect the points.
Explaining the Results
The line graph helps us visualize the relationship between the x– and y-coordinates. In this example, the y-coordinate is always twice as large as the x-coordinate. Another way to express the relationship is to say the terms in pattern y are 2 times as much as the terms in pattern x. You could also express the relationship as
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Use the rules to complete the chart below.
Describe the relationship between the two sequences.
Answer
Sequence 2 is 3 times the size of Sequence 1.
| Sequence 1 Rule: Add 2 |
Sequence 2: Rule: Add 6 |
| 2 | 6 |
| 4 | 12 |
| 6 | 18 |
| 8 | 24 |
Which coordinates represent 2 other points that fall on the line represented
in the chart below. Use the graph to show your work.
A. (9, 12) and (15, 18)
B. (9, 12) and (12, 14)
C. (12, 18) and (24, 36)
D. (12, 18) and (18, 21)
| Point | x | y |
| A | 0 | 3 |
| B | 3 | 6 |
| C | 6 | 9 |
Answer
A
The rule is add 3 for both the x– and y-coordinates.
Complete the table below. Then explain the relationship between the x-coordinates
and y-coordinates.
Answer
y is 2 more than x or y = x + 2. The coordinate pairs are created using the numbers in the x and y columns.
| Point | X | Y | (x, y) |
| A | 1 | 3 | (1, 3) |
| B | 3 | 5 | (3, 5) |
| C | 6 | 8 | (6, 8) |
| D | 9 | 11 | (9, 11) |
Which statement describes the relationship between the two lines shown the
graph below.
A. Line b is steeper than Line a
B. The y-coordinates in Line a are twice as large as the y-coordinates in Line b
C. Line a and Line b are perpendicular
D. Line a and Line b are parallel
Answer
B
First list the ordered pairs. Then, determine the relationship.
How are (1, 7) and (7, 1) different when plotted on the coordinate plane?
Answer
The first number in each coordinate pair tells you how far to travel on the x-axis. The second number tells you how far to travel up the y-axis. Do this for both points.
Click on the quizzes below to test your knowledge.
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