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=
.
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Answered by
GPT 3.5
To determine the rate of change, we need to find the slope of the line passing through the points (2,22) and (8,25).
First, calculate the change in y: 25 - 22 = 3
Next, calculate the change in x: 8 - 2 = 6
Now, we can calculate the rate of change (slope):
m = (change in y)/(change in x) = 3/6 = 0.5
Therefore, the rate of change is m= 0.5.
To find the initial value (y-intercept), we can substitute one of the points into the slope-intercept form of a linear equation, y = mx + b.
Using the point (2,22):
22 = 0.5(2) + b
22 = 1 + b
b = 21
Therefore, the initial value is b= 21.
First, calculate the change in y: 25 - 22 = 3
Next, calculate the change in x: 8 - 2 = 6
Now, we can calculate the rate of change (slope):
m = (change in y)/(change in x) = 3/6 = 0.5
Therefore, the rate of change is m= 0.5.
To find the initial value (y-intercept), we can substitute one of the points into the slope-intercept form of a linear equation, y = mx + b.
Using the point (2,22):
22 = 0.5(2) + b
22 = 1 + b
b = 21
Therefore, the initial value is b= 21.
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