Question

x | y
2 | 22
8 | 25

Determine the rate of change and the initial value of 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 the slope of a line:

Slope = (y2 - y1) / (x2 - x1)

Using the values from the table:
x1 = 2, y1 = 22
x2 = 8, y2 = 25

Slope = (25 - 22) / (8 - 2)
Slope = 3 / 6
Slope = 0.5

The rate of change, or slope, of the linear function is 0.5.

To find the initial value, we can substitute the values of x and y from one of the points into the equation of a line (y = mx + b) and solve for b:

Using the point (2, 22):
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21

Therefore, the initial value of the linear function is 21.