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cleanup and formatting with a few clarifications
\label{Numerical_Response_Advanced_Example}
%
\begin{figure}
\begin{center}\includegraphics[ width=0.80\paperwidth]{numericalResponseSlopeProblem}\end{center}
\caption{Slope Problem Parameters\label{Slope Problem Parameters Figure}}
\end{figure}
Now you have all the tools to create those wonderful dynamic, randomized problems that you've seen in
LON-CAPA. Consider a Numerical Response problem where the equations for two lines are randomly generated
and the students are asked to find the intercept. Try filling out your problem with the parameters shown
in Figure \ref{Slope Problem Parameters Figure}.
When creating randomized problems, you want to make sure that the problems
always have an answer. Consider what might happen if two
slopes are chosen, \emph{both} with the expression \texttt{\&random(-1.0,1.0,.2)}. One
out of ten students would get a problem where both slopes were equal, which
has either no solution (for unequal y-intercepts) or an infinite number of
solutions (for equal slopes and y-intercepts). Both of these cause a division-by-zero
error on the division that computes the answer. There are many ways to avoid
this, one of the easiest of which is picking one slope negative and one positive.
This same problem can show up in many other places as well, so be careful.
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