Question

Use the table names for the question x2, 8y22, 25 determine the rate of change and the initial value of the linear function given here is the table of values the rate of change is m and the value is b

Answer 1

To find the rate of change (m) and initial value (b) of the linear function, we need to identify two points from the table.

Let's take the points (x1, y1) = (2, 8) and (x2, y2) = (25, 22).

The rate of change (m) is given by:
m = (y2 - y1) / (x2 - x1)
m = (22 - 8) / (25 - 2)
m = 14 / 23
m = 0.6087

The initial value (b) can be calculated using the formula:
b = y1 - m * x1
b = 8 - 0.6087 * 2
b = 8 - 1.2174
b = 6.7826

Therefore, the rate of change (m) is 0.6087 and the initial value (b) is 6.7826 for the linear function given by the table.