Question

Use the table to answer the question.

x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.


The rate of change is m=, and the initial value is b=

Answer 1

To find the rate of change (m) of the linear function, we can use the formula:

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

Using the values from the table:
x1 = 1, y1 = 4
x2 = -3, y2 = 8

m = (8 - 4) / (-3 - 1)
m = 4 / -4
m = -1

So, the rate of change of the linear function is -1.

To find the initial value (b) of the linear function, we can use the formula for the slope-intercept form of a linear equation:

y = mx + b

Using the values from the table (e.g., x = 1, y = 4):

4 = -1(1) + b
4 = -1 + b
b = 4 + 1
b = 5

So, the initial value of the linear function is 5.