Problem

Determine if the function is linear:
Function 3
\begin{tabular}{|c|c|}
\hline$x$ & $y$ \\
\hline 2 & 0 \\
\hline 5 & 4 \\
\hline 8 & 8 \\
\hline 11 & 12 \\
\hline
\end{tabular}

Linear
Not linear

Answer

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Answer

Final Answer: The function is \(\boxed{\text{linear}}\).

Steps

Step 1 :Determine if the function is linear by checking if the difference in the y-values divided by the difference in the x-values (the slope) is constant for all pairs of points.

Step 2 :Calculate the slope between the first two points (2,0) and (5,4). The slope is \(\frac{4-0}{5-2} = 1.3333333333333333\).

Step 3 :Calculate the slope between the second pair of points (5,4) and (8,8). The slope is \(\frac{8-4}{8-5} = 1.3333333333333333\).

Step 4 :Calculate the slope between the third pair of points (8,8) and (11,12). The slope is \(\frac{12-8}{11-8} = 1.3333333333333333\).

Step 5 :Since the slope is the same for all pairs of points, the function is linear.

Step 6 :Final Answer: The function is \(\boxed{\text{linear}}\).

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