compare the linear function and the arithmetic sequence below.

linear function
x
-1,0,1,2

y
10,14,18,22

the rate of change of the linear function is

the y intercept of the linear function is

1 answer

The linear function can be written as y = 4x + 14.

The rate of change of the linear function is the coefficient of x, which is 4.

The y-intercept of the linear function is the y-value when x = 0, which is 14.

Arithmetic sequence:
-1, 0, 1, 2

In an arithmetic sequence, each term is obtained by adding a common difference to the previous term.

The common difference in this arithmetic sequence is 1.

Comparing the linear function and the arithmetic sequence:

In the linear function, the rate of change is constant and equal to 4. In the arithmetic sequence, the common difference is 1, which means that each term increases by 1 from the previous term. So, the rate of change in the linear function is greater than the rate of change in the arithmetic sequence.

In the linear function, the y-intercept is 14. In the arithmetic sequence, there is no y-intercept as it represents a sequence of x-values.

Overall, the linear function and the arithmetic sequence differ in terms of their rate of change and the concept of a y-intercept.