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
Solution
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 \(\boxed{\text{linear}}\).
