Question

is the function represented by the table non-linear?

\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 6 & 4 \\\\ \\hline 7 & 2 \\\\ \\hline 8 & 0 \\\\ \\hline 9 & -2 \\\\ \\hline \\end{array}$$

• yes, because it has a constant rate of change.
• yes, because it does not have a constant rate of change.
• no, because it has a constant rate of change.
• no, because it does not have a constant rate of change.

Explanation:

Calculate the rate of change between consecutive points

$$
LATEXBLOCK0
$$

Determine if the function is linear

$$ \text{Since } m_1 = m_2 = m_3 = -2, \text{ the rate of change is constant.} $$

$$ \text{A constant rate of change means the function is linear.} $$

$$ \text{Therefore, the function is NOT non-linear.} $$

Answer:

• Yes, because it has a constant rate of change.
• Yes, because it does not have a constant rate of change.
• No, because it has a constant rate of change. (Correct answer)
• No, because it does not have a constant rate of change.