To determine the linear function (Y = mX + b) from the given data, follow these steps:

Step 1: Identify the slope ((m))

The slope is calculated as (\frac{\Delta Y}{\Delta X}). Using points ((0,100)) and ((1,90)):
[m = \frac{90 - 100}{1 - 0} = -10]

Step 2: Find the y-intercept ((b))

The y-intercept is the value of (Y) when (X=0). From the table, when (X=0), (Y=100), so (b=100).

Step 3: Write the linear function

Substitute (m=-10) and (b=100) into (Y = mX + b):

Answer: (Y = -10X + 100)

(\boxed{Y=-10X+100})

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