To solve this question, we need to:
a. State two relationships about the relation.
To identify the relationships, we look at the pattern of the given ordered pairs. We have:
(5, 25)
(6, 30)
(7, 35)
(8, 40)
Let's examine the given ordered pairs more closely:
- From (5, 25) to (6, 30), the increment in the first number (which we'll call 'x') is 1 and the corresponding increment in the second number (which we'll call 'y') is 5.
- From (6, 30) to (7, 35), again the increment in 'x' is 1 and the increment in 'y' is 5.
- This same pattern occurs from (7, 35) to (8, 40).
This suggests two distinct relationships:
1. The first relationship is a proportional relationship where 'y' is 5 times 'x'. In mathematical terms, this can be expressed as y = 5x.
2. The second relationship is a consistent increase: whenever 'x' increases by 1, 'y' increases by 5. This is a linear relationship with a slope of 5.
b. Assuming the relation continues with the same relationship, state the two sets of ordered pairs that follow (8,40).
To predict the next two ordered pairs, we use the second relationship stated above (for each increase of 1 in 'x', 'y' increases by 5).
So, for the pair following (8,40):
- Increase 'x' (which is currently 8) by 1, giving us 8 + 1 = 9.
- Since 'y' increases by 5 for each increase in 'x', the new value of 'y' would be 40 + 5 = 45.
The first new ordered pair is (9, 45).
Now, for the pair after (9,45):
- Increase 'x' (which is currently 9) by 1, giving us 9 + 1 = 10.
- Once more, increase 'y' by 5 which results in 45 + 5 = 50.
The second new ordered pair is (10, 50).
In conclusion, the two sets of ordered pairs that follow (8, 40) are (9, 45) and (10, 50).
