what is the rule?
x 5 7 9 11
y 1 1.6 1.8 2.2
To determine the rule for the given sequence of numbers:
1. Look for a pattern in the relationship between the x-values and y-values.
2. Calculate the differences or ratios between consecutive x-values and y-values.
3. Identify any consistent pattern in these differences or ratios.
Let's examine the differences between consecutive x-values:
7 - 5 = 2
9 - 7 = 2
11 - 9 = 2
We observe that the differences between consecutive x-values are all 2.
Now, let's examine the differences between consecutive y-values:
1.6 - 1 = 0.6
1.8 - 1.6 = 0.2
2.2 - 1.8 = 0.4
Here, the differences between consecutive y-values are not consistent.
Since the differences between consecutive x-values are consistent (2), we can conclude that the rule for this sequence is adding 2 to each x-value to get the corresponding y-value.
Therefore, the rule is:
y = x + 2