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- documentclass{article}
- usepackage[margin=2.4cm]{geometry}
- usepackage{multicol}
- usepackage{tikz}
- usepackage{amsmath}
- usepackage[no-math]{fontspec}
- setmainfont{Times New Roman}
- usetikzlibrary{arrows}
- pagestyle{empty}
- setlength{columnsep}{3cm}
- begin{document}
- begin{multicols}{2}
- begin{enumerate}
- item[9.] $xy=0Leftrightarrow x=0 ; text{or} ; y=0.$ the graph consist of the cordinate axes\
- begin{tikzpicture}[>=triangle 45,x=0.5cm,y=0.5cm]
- clip(-4,-4) rectangle (4,4);
- draw [->] (0,-4.0) -- (0,4);
- draw [->] (-4,0) -- (4,0);
- draw [<-](0,1.5)--(1.5,2) node[anchor=west] {$xy=0$};
- draw [->] (2.5,1.5) -- (1.8,0);
- draw (4,0) node[anchor=north east] {$x$};
- draw (0,4) node[anchor=north east] {$y$};
- draw (0,0) node[anchor=north east] {$0$};
- end{tikzpicture}
- item[10.] $|y|=1 Leftrightarrow y=1 ;text{or} ; y=-1$\
- vspace{5mm}
- begin{tikzpicture}[>=triangle 45,x=0.5cm,y=0.5cm]
- clip(-4,-4) rectangle (4,4);
- draw [->] (0,-4.0) -- (0,4);
- draw [->] (-4,0) -- (4,0);
- draw (-4,2)--(0,2)node[anchor=north east] {$1$}--(4,2);
- draw (-4,-2)--(0,-2)node[anchor=north east] {$-1$}--(4,-2);
- draw (2,1) node {$|y|=1$};
- draw (4,0) node[anchor=north east] {$x$};
- draw (0,4) node[anchor=north east] {$y$};
- draw (0,0) node[anchor=north east] {$0$};
- end{tikzpicture}
- end{enumerate}
- end{multicols}
- begin{enumerate}
- item[11.]By the point-slop form of the equation of a line, an equation of the line throuth $(2,-3)$ with slope $6$ is\
- $y-(-3)=6(x-2)quad text{or} quad y=6x-15.$
- item[12.]$y-(-5)=-frac{7}{2}[x-(-3)]quad text{or} quad y=-frac{7}{2}x-frac{31}{2}$
- item[13.]The slope of the line throuth $(2,2)$ and $(1,6)$ is $m=dfrac{6-1}{1-2}=-5$, so an equation of the line is \
- $y-1=-5(x-2)quad text{or} quad y=-5x+11.$
- item[14.]For $-1,-2)$ and $(4,3)$, $m=dfrac{3-(-2)}{4-(-1)}=1$.An equation of the line is $y-3=1(x-4);text{or}; y=x-1.$
- end{enumerate}
- end{document}
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