Question

Create a function rule for the following:

x 0 3 6
f(x) -5 -3 -1

Answer 1

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

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.