Explain how to write a function rule from the table below (3

X |2|4|6|8|
Y |1|0|-1|

Hard to be sure, since you only give three values for y, but you can see that as x grows by 2, y decreases by 1`. So, the slope of the function is -1/2

So, start with y = -1/2 x

But that doesn't quite fit, since -1/2 (2) = -1, not 1.
So, how can you adjust y to make it fit?

notice that every time x increases by 2, y decreases by 1. So, a first guess would be

y = -1/2 x

But, -1/2 (2) = -1, and y(2) = 1, so we need to add 2 at the start. So,

y = 2 - 1/2 x

Check it out and you see it fits.

To write a function rule from the given table, you need to determine the relationship between the values in the X column and the values in the Y column. Here are the steps to write the function rule:

1. Look for patterns: Examine the changes in the Y values as the X values increase. In this case, as X increases by 2 (from 2 to 4 and from 4 to 6), the Y values decrease by 1 (from 1 to 0 and from 0 to -1). This suggests that X and Y have an inverse relationship.

2. Determine the mathematical operation: Since X and Y have an inverse relationship, we can deduce that the function involves multiplication or division. In this case, the Y values decrease by 1 every time the X values increase by 2. This indicates that we are dividing the X values by 2.

3. Establish the initial value: Find the Y value when X is equal to 2. In the given table, Y is 1 when X is 2.

4. Write the function rule: Based on the patterns identified, we can conclude that the function rule for this table is Y = -X/2 + 2.

By following these steps, you can write a function rule from a given table.