Find the rate of change from the table of values representing a linear function.
x 3 4 5 6
y 10 13 16 19
3
-3
2
1
The rate of change can be found by calculating the difference in y-values for each pair of consecutive x-values.
For the given table of values, the rate of change is as follows:
Rate of change between x = 3 and x = 4: y(4) - y(3) = 13 - 10 = 3
Rate of change between x = 4 and x = 5: y(5) - y(4) = 16 - 13 = 3
Rate of change between x = 5 and x = 6: y(6) - y(5) = 19 - 16 = 3
Therefore, the rate of change for the linear function represented by this table of values is 3.
To find the rate of change from the table of values, we need to calculate the difference in the y-values divided by the difference in the x-values.
Let's calculate the rate of change for each pair of consecutive points:
For the first pair (3, 10) and (4, 13):
Rate of change = (13 - 10) / (4 - 3) = 3 / 1 = 3
For the second pair (4, 13) and (5, 16):
Rate of change = (16 - 13) / (5 - 4) = 3 / 1 = 3
For the third pair (5, 16) and (6, 19):
Rate of change = (19 - 16) / (6 - 5) = 3 / 1 = 3
Therefore, the rate of change is 3 for all pairs of consecutive points in the table.