Patterns X and Y are generated using these rules.

Question

​Pattern X: Start with 0 and add 3.
Pattern Y: Start with 2 and add 2.
Which graph shows a set of points representing ordered pairs formed by corresponding terms in these two patterns?
A

B

C

D

Answer 1

To determine the ordered pairs formed by corresponding terms in Patterns X and Y, we first need to list the terms for both patterns.

Pattern X starts with 0 and adds 3:

• First term: 0
• Second term: 0 + 3 = 3
• Third term: 3 + 3 = 6
• Fourth term: 6 + 3 = 9
• Fifth term: 9 + 3 = 12
• Terms of Pattern X: 0, 3, 6, 9, 12

Pattern Y starts with 2 and adds 2:

• First term: 2
• Second term: 2 + 2 = 4
• Third term: 4 + 2 = 6
• Fourth term: 6 + 2 = 8
• Fifth term: 8 + 2 = 10
• Terms of Pattern Y: 2, 4, 6, 8, 10

Now, we can form the ordered pairs based on the corresponding terms in both patterns:

1. (0, 2)
2. (3, 4)
3. (6, 6)
4. (9, 8)
5. (12, 10)

The resulting set of ordered pairs is:

• (0, 2)
• (3, 4)
• (6, 6)
• (9, 8)
• (12, 10)

Next, you would need to look at the graphs A, B, C, and D and find one that contains these points plotted accordingly. The correct graph will show these ordered pairs as coordinates on a Cartesian plane.

If you can't visually inspect the graphs, please describe the graphs to me, and I can help you determine which one matches!