Question

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

Answer 1

First let's assume that the table contains points on a straight line.  Then all we have to do is to determine the slope of that line.

Suppose we go from (0,3) to (7,-28.5).
                                           -28.5-3        -31.5
Then the slope, m, is m = ------------- = ---------- = - 9/2, or - 4.5.
                                              7-0              7

Let's check this result!

Suppose that y = mx + b governs the relationship between x and y.


Then y = -4.5x + b

suppose we find b by substituting the coordinates from the point (0,3):

3 = -4.5(0) + b

Then b = 3, and y = -4.5x + 3.  Does the point (-2,12) satisfy this equation?

Does 12 = -4.5(-2) + 3?  Does 12 = 9 + 3?  YES.

So y = -4.5x + 3 is the equation from which these points came, and the rate of change of y with respect to x is the slope m = -4.5, or m = -9/2.