Question

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$$\begin{array}{|c|c|} \\hline 2 & 120 \\\\ \\hline 3 & 180 \\\\ \\hline 4 & 240 \\\\ \\hline 5 & 300 \\\\ \\hline \\end{array}$$

a. it represents a linear function because there is a constant rate of change.
b. it represents a linear function because there is not a constant rate of change.
c. it represents a non-linear function because there is a constant rate of change.
d. it represents a non-linear function because there is not a constant rate of change.

Explanation:

⚡ Using what you learned: understanding linear functions

Step 1: Calculate the rate of change

Let the left column be \( x \) and the right column be \( y \). We calculate the rate of change \( \frac{\Delta y}{\Delta x} \) between consecutive rows:

$$ \frac{180 - 120}{3 - 2} = \frac{60}{1} = 60 $$

$$ \frac{240 - 180}{4 - 3} = \frac{60}{1} = 60 $$

$$ \frac{300 - 240}{5 - 4} = \frac{60}{1} = 60 $$

Step 2: Determine the function type

Since the rate of change is constant (\( 60 \)), the table represents a linear function.

Answer:

A It represents a linear function because there is a constant rate of change.