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Jul 11th, 2014
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  1. documentclass{article}
  2. usepackage[margin=2.4cm]{geometry}
  3. usepackage{multicol}
  4. usepackage{tikz}
  5. usepackage{amsmath}
  6. usepackage[no-math]{fontspec}
  7. setmainfont{Times New Roman}
  8. usetikzlibrary{arrows}
  9. pagestyle{empty}
  10.  
  11. setlength{columnsep}{3cm}
  12. begin{document}
  13. begin{multicols}{2}
  14.  
  15. begin{enumerate}
  16. item[9.] $xy=0Leftrightarrow x=0 ; text{or} ; y=0.$ the graph consist of the cordinate axes\
  17.  
  18. begin{tikzpicture}[>=triangle 45,x=0.5cm,y=0.5cm]
  19. clip(-4,-4) rectangle (4,4);
  20. draw [->] (0,-4.0) -- (0,4);
  21. draw [->] (-4,0) -- (4,0);
  22. draw [<-](0,1.5)--(1.5,2) node[anchor=west] {$xy=0$};
  23. draw [->] (2.5,1.5) -- (1.8,0);
  24. draw (4,0) node[anchor=north east] {$x$};
  25. draw (0,4) node[anchor=north east] {$y$};
  26. draw (0,0) node[anchor=north east] {$0$};
  27. end{tikzpicture}
  28.  
  29. item[10.] $|y|=1 Leftrightarrow y=1 ;text{or} ; y=-1$\
  30. vspace{5mm}
  31.  
  32. begin{tikzpicture}[>=triangle 45,x=0.5cm,y=0.5cm]
  33. clip(-4,-4) rectangle (4,4);
  34. draw [->] (0,-4.0) -- (0,4);
  35. draw [->] (-4,0) -- (4,0);
  36. draw (-4,2)--(0,2)node[anchor=north east] {$1$}--(4,2);
  37. draw (-4,-2)--(0,-2)node[anchor=north east] {$-1$}--(4,-2);
  38. draw (2,1) node {$|y|=1$};
  39. draw (4,0) node[anchor=north east] {$x$};
  40. draw (0,4) node[anchor=north east] {$y$};
  41. draw (0,0) node[anchor=north east] {$0$};
  42.  
  43. end{tikzpicture}
  44. end{enumerate}
  45. end{multicols}
  46. begin{enumerate}
  47. 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\
  48. $y-(-3)=6(x-2)quad text{or} quad y=6x-15.$
  49. item[12.]$y-(-5)=-frac{7}{2}[x-(-3)]quad text{or} quad y=-frac{7}{2}x-frac{31}{2}$
  50. 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 \
  51. $y-1=-5(x-2)quad text{or} quad y=-5x+11.$
  52. item[14.]For $-1,-2)$ and $(4,3)$, $m=dfrac{3-(-2)}{4-(-1)}=1$.An equation of the line is $y-3=1(x-4);text{or}; y=x-1.$
  53. end{enumerate}
  54. end{document}
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