Question

the table below represents a linear function. identify the rate of change of the function.

x	y
0	-3
4	-10
8	-17

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) of a linear function between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Choose two points from the table

Let's take the points \((-4, 4)\) and \((0, -3)\). Here, \(x_1=-4\), \(y_1 = 4\), \(x_2=0\), \(y_2=-3\).

Step3: Calculate the rate of change

Substitute the values into the formula: \(m=\frac{-3 - 4}{0 - (-4)}=\frac{-7}{4}=-\frac{7}{4}\).

We can verify with another pair of points, say \((0, -3)\) and \((4, -10)\). Then \(x_1 = 0\), \(y_1=-3\), \(x_2 = 4\), \(y_2=-10\). \(m=\frac{-10-(-3)}{4 - 0}=\frac{-7}{4}=-\frac{7}{4}\), which is consistent.

Answer:

\(-\frac{7}{4}\)