Question

Find the rate of change and the initial value of the linear function given as a table of values. (1 point) The rate of change is m= , and the initial value is b= .

Answer 1

To find the rate of change (m) and the initial value (b) of the linear function given as a table of values, we need to select two points from the table and use the formula for finding the slope of a line:

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

Let's say our two points are (x1, y1) and (x2, y2) from the table. We can plug in the values of these points into the formula to find the rate of change (m).

Then we can find the initial value (b) by using one of the points and the rate of change (m) in the equation of a line:

y = mx + b

Let's go through an example to demonstrate this process. Let's say the table of values is as follows:

x | y
2 | 5
4 | 9

We will choose the points (2, 5) and (4, 9) to find the rate of change and the initial value.

First, calculate the rate of change (m):

m = (9 - 5) / (4 - 2)
m = 4 / 2
m = 2

The rate of change (m) is 2.

Next, find the initial value (b) using one of the points and the rate of change (m). Let's use the point (2, 5):

5 = 2(2) + b
5 = 4 + b
b = 5 - 4
b = 1

The initial value (b) is 1.

Therefore, the rate of change is m = 2, and the initial value is b = 1 for the linear function represented by the table of values.