Question

the table below shows points that are included in the graph of f(x), a linear function. what is the rate of change of f(x)? the table has columns x and y with rows: x=-1, y=2; x=2, y=14; x=6, y=30.

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 \((-1, 2)\) and \((2, 14)\). Here, \(x_1=-1\), \(y_1 = 2\), \(x_2 = 2\), \(y_2=14\).

Step3: Calculate the rate of change

Substitute the values into the formula: \(m=\frac{14 - 2}{2 - (-1)}=\frac{12}{3}=4\).
We can also check with another pair, say \((2,14)\) and \((6,30)\). \(x_1 = 2\), \(y_1=14\), \(x_2 = 6\), \(y_2 = 30\). Then \(m=\frac{30 - 14}{6 - 2}=\frac{16}{4}=4\).

Answer:

4