Question

Functions Unit Test
5 of 155 of 15 Items






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.

(1 point)
The rate of change is m=
, and the initial value is b=
.

Answer 1

To determine the rate of change and initial value of the linear function, we can use the formula for finding the slope (rate of change) of a line passing through two points:

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

By selecting two points from the table, let's say (2, 22) and (8, 25), we can plug in these values into the formula:

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

So, the rate of change (slope) of the linear function is 0.5.

To find the initial value (y-intercept), we can use the formula for the equation of a line in slope-intercept form:

y = mx + b

Using one of the points, we can plug in the values and solve for b:

22 = 0.5(2) + b
22 = 1 + b
b = 21

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