Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The rate of change of the linear function is equal to the slope of the function. To find the slope, we can use the formula:

slope = (change in y)/(change in x)

Using the given points (-1, 7) and (1, 11), we can calculate the change in y and change in x:

change in y = 11 - 7 = 4
change in x = 1 - (-1) = 2

slope = 4/2 = 2

Therefore, the rate of change of the linear function is 2.

The y-intercept of the linear function is the value of y when x = 0. From the given points, we can see that when x = 0, y = 9. Therefore, the y-intercept of the linear function is 9.

For the arithmetic sequence, the rate of change (common difference) is given as 2.

The initial value of the arithmetic sequence is given as 9. This is the value of the first term of the sequence (a1).

Since the rate of change of the linear function is equal to the rate of change of the arithmetic sequence, the rate of change of the linear function is also 2.