To determine the rate of change (m) and the initial value (b), we can use the formula for the equation of a line: y = mx + b.
First, we need to find the rate of change (m). To do this, we subtract the y values and divide by the difference in x values:
m = (25-22) / (8-2)
m = 3 / 6
m = 0.5
Next, we can use one of the points (2, 22) to find the initial value (b). Using the formula y = mx + b, we can substitute the slope (m=0.5), the x value (2), and the y value (22) into the equation:
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the rate of change is m = 0.5 and the initial value is b = 21.
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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