\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{Ebrahim.O}
\pdfinfo{
  /Title (co-ordinate-geometry-and-simultaneous-equations.pdf)
  /Creator (Cheatography)
  /Author (Ebrahim.O)
  /Subject (Co-Ordinate Geometry \& Simultaneous Equations Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{1F3AC2}
\definecolor{LightBackground}{HTML}{F1F2FB}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Co-Ordinate Geometry \& Simultaneous Equations Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Ebrahim.O} via \textcolor{DarkBackground}{\uline{cheatography.com/133545/cs/27308/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Ebrahim.O \\
  \uline{cheatography.com/ebrahim-o} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 29th March, 2021.\\
   Updated 29th March, 2021.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.9862 cm} x{1.9908 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{{\bf{Sketching Straight Lines}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
Using x \& y intercepts | C cannot be equal to 0 & Gradient - intercept method \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
ax + by = c -{}-\textgreater{} e.g 2x - 5y = 10 & y = mx + c \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
y = 0 when solving x & Horizontal Line \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
2x - 0 = 10 & gradient = 0 \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
x = 5 & y = c \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
x = 0 when solving y & Vertical Line \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
2(0) - 5y = 10 & gradient = undefined \tn 
% Row Count 10 (+ 2)
% Row 7
\SetRowColor{white}
-5y = 10 & x = a \tn 
% Row Count 11 (+ 1)
% Row 8
\SetRowColor{LightBackground}
y = 10/-5 & a -{}-\textgreater{} x-intercept \tn 
% Row Count 13 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{y = -2} \tn 
% Row Count 14 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{0.8354 cm} x{1.04425 cm} x{1.00248 cm} x{1.29487 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Finding the equation of a straight line}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Gradient} + \seqsplit{y-intercept} & Gradient + a point (x1, y1) & 2 points (x1, y1) (x2, y2) & Distance between 2 points \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Sub into \seqsplit{equation} & Sub into equation & 1st find m & Sub into equation \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
y = mx + c & y - y1 = m(x - x1) & m = y2 - y1/x2 - x1 & AB = √(x2 - x1)$^{\textrm{2}}$ + (y2 - y1)$^{\textrm{2}}$ \tn 
% Row Count 9 (+ 3)
% Row 3
\SetRowColor{white}
Example & Example & 2nd sub into equation & Example \tn 
% Row Count 12 (+ 3)
% Row 4
\SetRowColor{LightBackground}
c = 5 | m = -1 & m = 2 | (2, -0.5) & y - y1 = m(x - x1) & A = (3, -5) | B = (-2, 1) \tn 
% Row Count 15 (+ 3)
% Row 5
\SetRowColor{white}
y = -1x + 5 & y + 0.5 = 2(x - 2) & Example & AB = √(-2 - 3)$^{\textrm{2}}$ + (1 - -5)$^{\textrm{2}}$ \tn 
% Row Count 18 (+ 3)
% Row 6
\SetRowColor{LightBackground}
 & y + 0.5 = 2x - 4 & (-1, 4) , (5, 2) & AB = √(-5)$^{\textrm{2}}$ + 6$^{\textrm{2}}$ \tn 
% Row Count 20 (+ 2)
% Row 7
\SetRowColor{white}
 & y = 2x - 4.5 & m = 2 - 4/3 - (-1) & AB = √25 + 36 \tn 
% Row Count 22 (+ 2)
% Row 8
\SetRowColor{LightBackground}
 &  & m = -2/4 -{}-\textgreater{} -1/2 & AB = √61 \tn 
% Row Count 24 (+ 2)
% Row 9
\SetRowColor{white}
 &  & y - 4 = -1/2(x - - 1) &  \tn 
% Row Count 27 (+ 3)
% Row 10
\SetRowColor{LightBackground}
 &  & y - 4 = - 1/2x - 1/2 &  \tn 
% Row Count 30 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{0.8354 cm} x{1.04425 cm} x{1.00248 cm} x{1.29487 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Finding the equation of a straight line (cont)}}  \tn
% Row 11
\SetRowColor{LightBackground}
 &  & y = - 1/2x + 7/2 &  \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}----}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.73926 cm} x{1.41887 cm} x{1.41887 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Middle point of a line}}  \tn
% Row 0
\SetRowColor{LightBackground}
Middle point of a line & Paralell Lines & \seqsplit{Perpendicular} Lines \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Sub into equation - i.e / means divide & Sub into equation & Sub into equation \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
M = (x1 + x2/2, y1 + y2/2) & m1 = m2 & m1 x m2 = -1 or m2 = 1/m1 \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
Example & Example - 1st find m (gradient) & Example - 1st find m (gradient) \tn 
% Row Count 11 (+ 3)
% Row 4
\SetRowColor{LightBackground}
(3, 5) | (2, 7) & A (4, 13) | B (2, 9) & A (-4, 9) | B (2, -6) \tn 
% Row Count 13 (+ 2)
% Row 5
\SetRowColor{white}
M = 3 + 2/2, 5 + 7/2 & mAB = 9 - 13/2 - 4 & mAB = -6 - 9/2 - (-4) \tn 
% Row Count 15 (+ 2)
% Row 6
\SetRowColor{LightBackground}
M = (5/2, 12/2) & mAB = -4/-2 & mAB = -15/6 \tn 
% Row Count 16 (+ 1)
% Row 7
\SetRowColor{white}
M = (5/2, 6) & mAB = 2 & mAB = -5/2 \tn 
% Row Count 17 (+ 1)
% Row 8
\SetRowColor{LightBackground}
 & C (0, -10) | D (15, 0) & C (-5, 8) | D (10, 14) \tn 
% Row Count 19 (+ 2)
% Row 9
\SetRowColor{white}
 & mCD = 0 - (-10)/15 - 0 & mCD = 14 - 8/10 - (-5) \tn 
% Row Count 21 (+ 2)
% Row 10
\SetRowColor{LightBackground}
 & mCD = 10/15 & mCD = 6/15 \tn 
% Row Count 22 (+ 1)
% Row 11
\SetRowColor{white}
 & mCD = 2/3 & mCD = 2/5 \tn 
% Row Count 23 (+ 1)
% Row 12
\SetRowColor{LightBackground}
 & ∵ mAB ≠ mCB & 2nd | sub into m1 x m2 = -1 \tn 
% Row Count 26 (+ 3)
% Row 13
\SetRowColor{white}
 & ∴ not parralell & -5/2 x 2/5 = -1 \tn 
% Row Count 28 (+ 2)
% Row 14
\SetRowColor{LightBackground}
 &  & -10/10 = -1 \tn 
% Row Count 29 (+ 1)
% Row 15
\SetRowColor{white}
 &  & ∴ AB ⊥ CD \tn 
% Row Count 31 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}