Question

Use the table to answer the question.
x | y
2 | 22
8 | 25

Determine the rate of change and the initial value of the linear function given here as a table of values.

Answer 1

To determine the rate of change and the initial value of the linear function, we can use the formula for a linear function:

y = mx + b

where m is the rate of change (or the slope) and b is the initial value (or the y-intercept).

Looking at the given table, we can see that the y-values change by 3 units when the x-values increase by 6 units. Therefore, the rate of change (m) is 3/6 = 1/2.

To find the initial value (b), we can use one of the points from the table. Let's use the first point (2, 22). Plugging it into the equation, we get:

22 = (1/2)(2) + b

Simplifying, we find:

22 = 1 + b

Subtracting 1 from both sides, we get:

b = 22 - 1 = 21

Therefore, the rate of change (m) of the linear function is 1/2 and the initial value (b) is 21.