Question

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

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

Answer 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?

Answer 2

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.