Create a function rule for the following: x 0 3 6 f (x) - 5 - 3 - 1

The function rule is y = (2/3) x - 5.

Step-by-step explanation:

Let's assume for now that the function is a linear one. Then y = mx + b.

As we move from (0, - 5) to (3, - 3), x increases by 3 and y increases by 2.

Thus, the slope of this line is m = rise / run = 2/3.

Then our y = mx + b becomes y = (2/3) x + b, or - 5 = (2/3) (0) + b.

Thus, b = - 5, and the equation is y = (2/3) x - 5.

Now let's check this result. When x = 6, does the equation predict y = - 1?

y = (2/3) (6) - 5 = 4 - 5 = - 1. YES

The function rule is y = (2/3) x - 5.