Question

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

x	y
0	2
4	7
8	12

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 \((-4, -3)\) and \((0, 2)\). Here, \(x_1=-4\), \(y_1 = - 3\), \(x_2=0\), \(y_2=2\).

Step3: Calculate the rate of change

Substitute the values into the formula: \(m=\frac{2-(-3)}{0 - (-4)}=\frac{2 + 3}{0+4}=\frac{5}{4}\).
We can also check with other points, say \((0, 2)\) and \((4, 7)\). Then \(m=\frac{7 - 2}{4-0}=\frac{5}{4}\), and with \((4, 7)\) and \((8, 12)\), \(m=\frac{12 - 7}{8 - 4}=\frac{5}{4}\).

Answer:

\(\frac{5}{4}\)