Question

Explain how to write a function rule from the table below. x :2 4 6 y :1 0 –1

Answer 1

To put it simple, y = 2 - 1/2 x

Answer 2

Our "y-intercept" (where x = 0) acts as the foundation of our function here.
We can extrapolate from what we have here...if x is 0, y is going to be 2.
So, we start at 2 for y, and every time we decrease x by 2, y increases by 1.
If we decrease x by just 1, y increases by ½.
This also goes in the opposite direction. Increase x by 1, decrease y by ½.
We can write the change in y as -½x.
That change is being added to our original value of 4, of course.
The equation of this line is $y=-\frac{1}2x+2$.