\documentclass[12pt]{article}\usepackage{ammaths}\en

\begin{document}

\module{Different types of line equations}{01}{17}{55 mins}

\prereq{Line equations.}

\object{\begin{itemize}
        \item Discover different types of line equations, and how they can be used.
	\item Practise the computations to switch from one kind to another.
	\end{itemize}}

\mater{\begin{itemize}
	\item Slideshow.
	\item Lesson.
	\item Answer sheet.
	\end{itemize}}

The class is divided into four teams. Each team is given an answer sheet where answers will be written for the three
parts. The two first parts are turn by turn games. The thrid part is a speed game.

\modpart{Recognize a form}{20 mins}

Turn by turn, each team is given (orally) an equation and has to find out what type it is and win  points for every good
answer. If a team gives a wrong answer, the next team can answer and win 3 points, and so on.

\begin{center}
\begin{tabular}{|c|c|c|c|} \hline
$\Delta_1$ &  $y=-4x$ & $\Delta_2$ & $\frac{x}{-2}+\frac{y}{5}=1$\\ \hline
$\Delta_3$ &  $7x+3y-8=0$ & $\Delta_4$ & $y-5=-3(x-2)$\\ \hline
$\Delta_5$ &  $\frac{x}{\frac13}+\frac{y}{-3}=1$ & $\Delta_6$ & $x+\sqrt{5}y-3=0$\\ \hline
$\Delta_7$ &  $y+1=-\frac{1}{2}(x+5)$ & $\Delta_8$ & $y=-7(x+8)$\\ \hline
\end{tabular}
\end{center}

\modpart{Switch from one form to another}{25 mins}

Four line equations are given. Teams have 10 minutes or so to convert these equations to, the three other forms. Teams
are then asked to fill one line, turn by turn, one line for each team. Four points are awarded for every good answer. If
a team gives a wrong answer, the next team can answer and win 3 points, and so on.

\begin{center}
\begin{tabular}{|c|c|c|c|c|} \hline
 & General form & Slope-intercept form & Point-intercept form & Intercept form \\ \hline
$d_1$ & $\star$ $3x-3y+3=0$ & $y=x+1$ & $y+1=1(x-(-2))$  & $\frac{x}{-1}+\frac{y}{1}=1$ \\ \hline
$d_2$ & $x-y-3=0$ & $y=x-3$ & $y-0=1(x-3)$ &  $\star$ $\frac{x}{3}+\frac{y}{-3}=1$ \\ \hline
$d_3$ & $2x+5y-10=0$ & $y=-\frac25x+2$ & $y-0=-\frac25(x-5)$ & $\star$ $\frac{x}{5}+\frac{y}{2}=1$ \\ \hline
$d_4$ & $6x-y-11=0$ & $\star$  $y=6x-11$ & $y-1=6(x-2)$ & $\frac{x}{\frac{11}{6}}+\frac{y}{-11}=1$ \\ \hline
\end{tabular}
\end{center}


\modpart{Computations -- Speed game}{Remaining time.}

Four questions are asked about the lines  in the previous part. The first team to rise all their hands can answer and
get 10 points. If the answer is wrong, another team and answer and win 8 points, and so on.

\begin{enumerate}
\item Draw the lines $d_1$ and $d_2$ on a coordinate graph.
\item Find two points on each of the lines $d_3$ and $d_4$.
\item Compute the $x$-intercept of the lines $d_1$ and $d_2$.
\item Are there two parallel lines among these eight lines ?
\end{enumerate}

\pagebreak

\moddocdis{Different types of line equations}{01}{17}{Lesson}

Every straight line has an infinite number of cartesian
equations, all equivalent but sometimes very different in the way
they look and the information they directly present. Here are the
main kinds of equations. Only the two first kinds are commonly used
in France, but the others are quite interesting too.

\begin{itemize}
\itemb The general form : $ax+by+c=0$, where $a$, $b$ and $c$ are
three real numbers. Any line has an equation of this form, and
indeed many as it's always possible to apply a coefficient to the
whole equation.
\itemb Slope-intercept form : $y=mx+p$, where $m$ and $p$ are real
numbers, $m$ being the slope and $p$ the intercept. This form is
unique for any line not parallel to the $y$-axis.
\itemb Point-slope form : $y-y_0=m(x-x_0)$, where $m$ is a real
number, the slope, and $(x_0,y_0)$ is a couple of real numbers, the
coordinates of a point on the line. This form is not unique, as any
point on the line can be used.
\itemb Intercept form : $\dis\frac{x}{q}+\dis\frac{y}{p}=1$, where
$p$ and $q$ are real nonzero numbers, respectively the $y$-intercept
and the $x$-intercept.
\end{itemize}

\bigskip

It's easy to switch from one form to another, as illustrated in the
example below :
\begin{eqnarray*}
4x+2y-6 &=& 0 \textsf{ (General form)} \\
2y &=& -4x+6\\
y &=& -2x+3 \textsf{ (Slope-intercept form)}\\
y &=& -2(x-1)+1\\
y-1 &=& -2(x-1) \textsf{ (Point-slope form)}\\
2x+y &=& 3 \\
\frac{2x}{3}+\frac{y}{3} &=& 1 \\[5pt]
\frac{x}{\frac{3}{2}}+\frac{y}{3} &=& 1  \textsf{ (Intercept form)}
\end{eqnarray*}


\pagebreak

\moddocdis{Different types of line equations}{01}{17}{Answer sheet}

\large

\sectionblack{Part 1 -- Recognize a form}

\begin{center}
\begin{tabular}{|c|c|} \hline
Line & Form \\ \hline
$\Delta_1$ & \rule{10cm}{0pt} \\[7pt] \hline
$\Delta_2$ &  \\[7pt] \hline
$\Delta_3$ &  \\[7pt] \hline
$\Delta_4$ &  \\[7pt] \hline
$\Delta_5$ &  \\[7pt] \hline
$\Delta_6$ &  \\[7pt] \hline
$\Delta_7$ &  \\[7pt] \hline
$\Delta_8$ &  \\[7pt] \hline
\end{tabular}
\end{center}



\sectionblack{Part 2 -- Switch from one form to the others}

\begin{center}\hspace*{-1cm}
\begin{tabular}{|c|c|c|c|c|} \hline
Line & General form & Slope-intercept form & Point-slope form & Intercept form\\ \hline
$d_1$ & &&& \\[7pt] \hline
$d_2$ & &&&\\[7pt] \hline
$d_3$ & &&& \\[7pt] \hline
$d_4$ & &&& \\[7pt] \hline
\end{tabular}
\end{center}

\pagebreak

\sectionblack{Part 3 -- Use the best form to carry out a computation}

\begin{enumerate}
\item Coordinate graph :
\begin{center}
\psset{xunit=0.8cm,yunit=0.8cm}\small
\begin{pspicture*}(-5.09,-5.5)(5.28,5.5)
\psgrid[subgriddiv=0,gridlabels=0,gridcolor=lightgray](0,0)(-5.09,-5.06)(5.28,5.07)
\psset{xunit=0.8cm,yunit=0.8cm,algebraic=true,dotstyle=*,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
\psaxes[xAxis=true,yAxis=true,Dx=1,Dy=1,ticksize=-2pt 0,subticks=2]{->}(0,0)(-5.09,-5.06)(5.28,5.07)
\end{pspicture*}
\end{center}
\item\begin{tabular}{|c|p{4cm}|p{4cm}|} \hline
$d_3$ &  &\\[7pt] \hline
$d_4$ &  &\\[7pt] \hline
\end{tabular}\bigskip
\item \begin{tabular}{|c|p{4cm}|p{4cm}|} \hline
$d_1$ &  &\\[7pt] \hline
$d_2$ &  &\\[7pt] \hline
\end{tabular}
\item \dotfill\rule{0pt}{25pt} 
\end{enumerate}

\end{document}
