Answer:
y = -5x - 1
Explanation:
Note that as x increases from -2 to -1, y decreases from 9 to 4, a drop of 5.
Similarly, if x increases from 0 to 1, y decreases from -1 to -6, a drop of 5.
Thus, this table represents a decreasing linear function.
The slope of this line is m = rise / run = -5 / 1, or just -5.
Using the point-slope formula for the equation of a straight line:
y -k = m(x - h). Here, the slope, m, is -5, and one point on the line is (0, -1).
Thus, we have y + 1 = -5(x - 0), or y = -5x - 1.
The "function rule" here is y = -5x - 1, a linear function.