To find the rate of change from the table you provided, we can calculate the difference in the values for each consecutive pair of x-values (the first column) and their corresponding y-values (the second column).
Here's the data presented in the table:
x | y
-----
1 | 12
2 | 19
3 | 26
4 | 33
5 | 40
6 | 47
Now let's calculate the differences in y-values for consecutive x-values:
- From x = 1 to x = 2: \( 19 - 12 = 7 \)
- From x = 2 to x = 3: \( 26 - 19 = 7 \)
- From x = 3 to x = 4: \( 33 - 26 = 7 \)
- From x = 4 to x = 5: \( 40 - 33 = 7 \)
- From x = 5 to x = 6: \( 47 - 40 = 7 \)
The rate of change (slope) between the x and y values is consistent at 7 for each interval. This means that for each increase of 1 in x, y increases by 7.