Question

what is the rate of change of the linear function represented by the table?

\\(\

$$\begin{array}{|c|c|}\\hline x & f(x) \\\\\\hline -2 & -13 \\\\\\hline -1 & -10 \\\\\\hline 0 & -7 \\\\\\hline 1 & -4 \\\\\\hline 2 & -1 \\\\\\hline\\end{array}$$

\\)

• \\(\frac{1}{3}\\)
• \\(\frac{1}{2}\\)
• 2
• 3

Explanation:

Identify coordinates from the table

Using the Average Rate of Change and Slope Formula knowledge points

We select two points from the table:

$$ (x_1, y_1) = (-2, -13) $$

$$ (x_2, y_2) = (-1, -10) $$

Calculate the rate of change

Using the Slope Formula knowledge point

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-10 - (-13)}{-1 - (-2)} = \frac{3}{1} = 3 $$

Answer:

• (A) \(\frac{1}{3}\)
• (B) \(\frac{1}{2}\)
• (C) 2
• (D) 3 (Correct answer)