What is the rate of change of y with respect to x for this function?

The rate of change of y with respect to x for the given function with coordinates expressed in the table is; dy/dx = -9/2

The rate of change of y with respect to x for a given linear function is simply the slope expressed as;

dy/dx = (y2 - y1)/(x2 - x1)

Let us take the first 2 coordinates which are;

(-2, 12) and (0, 3)

Thus;

dy/dx = (3 - 12)/(0 - (-2))

dy/dx = -9/2

Or dy/dx = -4.5

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bearing in mind that the average rate of change = slope, and for that we can simply use two points off the table.

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3