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

Answer 1

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 :)