Compare the linear function and the arithmetic sequence below.

Linear Function

x y
-1 7
0 9
1 11
2 13
The rate of change of the linear function is

The y-intercept of the linear function is

Arithmetic Sequence:

an = 9 + (n−1)(2)
The rate of change (common difference) of the arithmetic sequence is

The initial value of the arithmetic sequence is

The rate of change of this linear function is
the rate of change of this arithmetic sequence.

Arithmetic sequences
can be represented as a linear function.

1 answer

The rate of change of the linear function is the difference in the y-values over the difference in the x-values. In this case, the difference in y-values is 2 and the difference in x-values is 1. Therefore, the rate of change is 2/1 = 2.

The y-intercept of the linear function is the value of y when x is 0. In this case, when x is 0, y is 9. Therefore, the y-intercept is 9.

The rate of change (common difference) of the arithmetic sequence is the difference between consecutive terms. In this case, the common difference is 2.

The initial value of the arithmetic sequence is the value when n is 1. Plugging in n=1 into the sequence formula, we get a1 = 9 + (1-1)(2) = 9. Therefore, the initial value is 9.

The rate of change of this linear function is the same as the rate of change (common difference) of the arithmetic sequence. In this case, both are 2.