Х 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.
To determine the rate of change, we can find the difference in the y-values divided by the difference in the x-values for any two points. Let's choose the points (2, 22) and (8, 25) from the table.
Rate of Change = (Change in y) / (Change in x)
= (25 - 22) / (8 - 2)
= 3 / 6
= 0.5
Therefore, the rate of change of the linear function is 0.5.
To determine the initial value, we can substitute any of the points into the equation y = mx + b, where m is the rate of change and b is the initial value. Let's use the point (2, 22).
22 = 0.5 * 2 + b
22 = 1 + b
b = 21
Therefore, the initial value of the linear function is 21.