problem: Of the four points $(2,2)$, $(9,11)$, $(5,7)$, and $(11,17)$, three lie on the same line. Which point is not on the line?
solution: Consider points $P$, $Q$, and $R$. If the slope between point $P$ and point $Q$ is the same as the slope between point $Q$ and point $R$, $P$, $Q$, and $R$ are collinear. So we must find the slopes between every pair of possible points. Let us name the points: $A=(2,2)$, $B=(9,11)$, $C=(5,7)$, and $D=(11,17)$. We make a chart of all possible pairs of points and calculate the slope:
  
  \begin{tabular}{c|c}
  Points& Slope \\ \hline
  \vspace{0.05in} A,B&$\frac{11-2}{9-2}=\frac{9}{7}$\\ \vspace{0.05in}
  $A,C$&$\frac{7-2}{5-2}=\frac{5}{3}$\\ \vspace{0.05in}
  $A,D$&$\frac{17-2}{11-2}=\frac{15}{9}=\frac{5}{3}$\\ \vspace{0.05in}
  $B,C$&$\frac{7-11}{5-9}=\frac{-4}{-4}=1$\\ \vspace{0.05in}
  $B,D$&$\frac{17-11}{11-9}=\frac{6}{2}=3$\\ \vspace{0.05in}
  $C,D$&$\frac{17-7}{11-5}=\frac{10}{6}=\frac{5}{3}$
  \end{tabular}As we can see, the slopes between $A$ and $C$, $A$ and $D$, and $C$ and $D$ are the same, so $A$, $C$, and $D$ lie on a line, Thus $B$, or the point $\boxed{(9,11)}$, is not on the line.