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\begin{document}
\noindent Name: \rule{7cm}{.2pt} \vspace{.3cm} \hfill Date:  \rule{3.5cm}{.2pt}
\vspace{.3cm}

\noindent\hrulefill
\begin{center}
{\bf \Large{MA 162}} \\\vspace{.1cm} Week 2 Recitation Worksheet (Thursday)
\end{center}
\vspace{-.3cm}
\hrulefill

\begin{center}
\fbox{\textbf{You must show all work to receive full credit.}}
\end{center}

\begin{enumerate}
%1
\item Graph the line $4x - 9y = 18$ by finding the intercepts.
\begin{figure}[h]
	\begin{minipage}{.5\textwidth}
		\hspace{0.9cm}$x$-intercept:  \underline{\hspace{3cm}}\vspace{3cm}
		
		\hspace{0.9cm}$y$-intercept:  \underline{\hspace{3cm}}\vspace{3.1cm}
    \end{minipage}%
    \begin{minipage}{0.5\textwidth}
        \begin{tikzpicture}[scale=0.6]
			\draw[help lines] (-5.5,-5.5) grid (5.5,5.5);
			\draw[ultra thick,<->] (-6,0) -- (6,0) node[right] {$x$};
			\draw[ultra thick,<->] (0,-6) -- (0,6) node[above] {$y$};
			\foreach \x in {1,2,...,5} { \draw[thick] ( \x,0.2) -- ( \x,-0.2) ( \x,0) +(0,-0.10) node[below] {$\x$}; }
			\foreach \y in {1,2,...,5} { \draw[thick] (0.2, \y) -- (-0.2, \y) (0, \y) +(-0.10,0) node[left]  {$ \y$}; }
			\foreach \x in {1,2,...,5} { \draw[thick] (-\x,0.2) -- (-\x,-0.2) (-\x,0) +(0,-0.10) node[below] {$-\x$}; }
			\foreach \y in {1,2,...,5} { \draw[thick] (0.2,-\y) -- (-0.2,-\y) (0,-\y) +(-0.10,0) node[left]  {$-\y$}; }
		\end{tikzpicture}
    \end{minipage}
\end{figure}\vspace{1cm}


%2
\item Graph the line $2x + 3y = 0$ by first determining two points that satisfy the equation.
\begin{figure}[h]
	\begin{minipage}{.5\textwidth}
		\hspace{0.9cm}Point 1:  \underline{\hspace{3cm}}\vspace{3cm}
		
		\hspace{0.9cm}Point 2:  \underline{\hspace{3cm}}\vspace{3.1cm}
    \end{minipage}%
    \begin{minipage}{0.5\textwidth}
		\begin{tikzpicture}[scale=0.6]
			\draw[help lines] (-5.5,-5.5) grid (5.5,5.5);
			\draw[ultra thick,<->] (-6,0) -- (6,0) node[right] {$x$};
			\draw[ultra thick,<->] (0,-6) -- (0,6) node[above] {$y$};
			\foreach \x in {1,2,...,5} { \draw[thick] ( \x,0.2) -- ( \x,-0.2) ( \x,0) +(0,-0.10) node[below] {$\x$}; }
			\foreach \y in {1,2,...,5} { \draw[thick] (0.2, \y) -- (-0.2, \y) (0, \y) +(-0.10,0) node[left]  {$ \y$}; }
			\foreach \x in {1,2,...,5} { \draw[thick] (-\x,0.2) -- (-\x,-0.2) (-\x,0) +(0,-0.10) node[below] {$-\x$}; }
			\foreach \y in {1,2,...,5} { \draw[thick] (0.2,-\y) -- (-0.2,-\y) (0,-\y) +(-0.10,0) node[left]  {$-\y$}; }
		\end{tikzpicture}
	\end{minipage}
\end{figure}


\newpage
%3
\item Graph the line that passes through the point $(-2,1)$ and has slope $m = -\dfrac{4}{3}$.
\begin{center}
	\begin{tikzpicture}[scale=0.6]
		\draw[help lines] (-5.5,-5.5) grid (5.5,5.5);
		\draw[ultra thick,<->] (-6,0) -- (6,0) node[right] {$x$};
		\draw[ultra thick,<->] (0,-6) -- (0,6) node[above] {$y$};
		\foreach \x in {1,2,...,5} { \draw[thick] ( \x,0.2) -- ( \x,-0.2) ( \x,0) +(0,-0.10) node[below] {$\x$}; }
		\foreach \y in {1,2,...,5} { \draw[thick] (0.2, \y) -- (-0.2, \y) (0, \y) +(-0.10,0) node[left]  {$ \y$}; }
		\foreach \x in {1,2,...,5} { \draw[thick] (-\x,0.2) -- (-\x,-0.2) (-\x,0) +(0,-0.10) node[below] {$-\x$}; }
		\foreach \y in {1,2,...,5} { \draw[thick] (0.2,-\y) -- (-0.2,-\y) (0,-\y) +(-0.10,0) node[left]  {$-\y$}; }
	\end{tikzpicture}
\end{center}\vspace{1cm}


%4
\item Find the slope of the line passing through the points $(6,3)$ and $(4,-2)$.\vfill


%5
\item A line with slope $m = -\dfrac{2}{7}$ passes through the points $(4,19)$ and $(x,15)$.   What is the value of $x$?\vfill


\newpage
%6
\item Find the slope and $y$-intercept of the line with equation
\begin{equation*}
11x-5y+1=-4x+7y+2.
\end{equation*}\vfill


%7
\item Find the slope-intercept form of the line that passes through the points $(-2,9)$ and $(6,-15)$.\vfill


%8
\item Are the points $(-1,-2)$ and $(9,-6)$ on the same side of the line $3x+5y=-7$?  How do you know?\vfill
\end{enumerate}
\end{document}