# 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.

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 |

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.

**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

B

First list the ordered pairs. Then, determine the relationship.

How are (1, 7) and (7, 1) different when plotted on the coordinate plane?

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.

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