To determine the rate of change of a linear function, we need to find the difference in the y-values divided by the difference in the x-values.
For the given table of values, the difference in the y-values is 25 - 22 = 3, and the difference in the x-values is 8 - 2 = 6.
Therefore, the rate of change is 3/6 = 1/2.
To determine the initial value of the linear function, we can use any point from the given table. Let's use the point (2, 22).
Using the slope-intercept form of a linear equation y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values of x, y, and the slope into the equation and solve for b.
22 = (1/2)(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value of the linear function is 21.
In conclusion, the rate of change of the linear function is 1/2 and the initial value is 21.
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.
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