explain how to write a function rule from the table below. then write a function rule
x- 2,4,6
y- 1, 0 , -1

Question

explain how to write a function rule from the table below. then write a function rule 
x- 2,4,6
y- 1, 0 , -1

cruffo · Answer

Note that the y-values go down 1 for every 2 right in x.  This is a linear function, y = mx + b.  The slope m = -1/2.  But we are not given the y-intercept directly.  However, if we extend the pattern "backwards" (or up1, left 2), we can get x = 0, y = 2.  So the model is 
$$y = -\frac{1}{2}x + 2$$

Checking:
(2,1): $1 = -\frac{1}{2}(2) + 2$ ... true :)
(4,0): $0 = -\frac{1}{2}(4) + 2$ ... true :)
(6,-1): $-1 = -\frac{1}{2}(6) + 2$ ... true :)