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NSW Y8 Maths

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NSW Y8 Maths Graphing Linear Equations Graphing Linear Equations

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Graphing Linear Equations Theory

\begin{multicols}{2} \textbf{Example 1}\\ From the table below, draw the graph of the line and state the equation of the line.\\ \begin{center} \begin{tabular}{|c|c|c|c|} \hline \(x\) & -1 & 0 & 1 \\ \hline \(y\) & 0 & 1 & 2 \\ \hline \end{tabular} \end{center} \hfill\linebreak \textbf{Example 1 solution}\\ \(y=mx+b\)\\ when \(x=0, \; y=1\)\\ \(\begin{aligned} \therefore 1 & =0+b \rightarrow b=1 \\ y & =m x+1 \end{aligned}\)\\ when \(x=1,\; y=2\)\\ \(\begin{aligned} \therefore 2 & =m+1 \\ \therefore m & =1 \\ \therefore y & =x+1 \end{aligned}\) \begin{center} \begin{tikzpicture}[scale=0.9] \def \xmax{3} \def \xmin{-3} \def \ymax{3} \def \ymin{-3} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis lines=middle, axis line style={shorten >=-10pt, shorten <=-10pt,very thick,Stealth-Stealth}, grid=both, %major, major grid style={line width=1pt,draw=black!70}, minor x tick num=4, minor y tick num=4, ylabel = $y$, xlabel = $x$, width=3in, height=3in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, axis on top=false, axis line style = thick, major tick style = thick, xtick distance = 1, xlabel style={at={(ticklabel* cs:1.05)},anchor=west}, x grid style={thin, opacity=0.5}, ytick distance = 1, ylabel style={at={(ticklabel* cs:1.05)},anchor=south}, y grid style={thin, opacity=0.5}, axis on top=false, xtick={-4,-3,-2,-1,0,1,2,...,4}, ytick={-4,-3,-2,-1,0,1,2,...,6}, nodes near coords style={ above right=3pt, inner sep=0, color=black, font=,}, ] \addplot[name path=a, ultra thick, latex-latex, samples=300, smooth, domain=-3:2, red] {\x+1} node [pos=0.9, left, red, font=\small] {}; \end{axis} \end{tikzpicture} \end{center} \columnbreak \textbf{Example 2}\\ From the table below, draw the graph of the line and state the equation of the line\\ \begin{center} \begin{tabular}{|l|l|l|l|} \hline \(x\) & -1 & 0 & 1 \\ \hline \(y\) & 5 & 3 & 1 \\ \hline \end{tabular} \end{center} \hfill \linebreak \textbf{Example 2 solution}\\ \(y=m x+b\)\\ when \(x=0, y=3\)\\ \(\begin{aligned} & 3=0+b \rightarrow b=3 \\ & y=m x+3 \end{aligned}\)\\ when \(x=1, y=1\)\\ \(\begin{aligned} \therefore 1 & =m+3 \\ m & =-2 \\ \therefore y & =-2 x+3 \end{aligned}\)\\ \begin{center} \begin{tikzpicture}[scale=0.9] \def \xmax{4} \def \xmin{-2} \def \ymax{5} \def \ymin{-2} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis lines=middle, axis line style={shorten >=-10pt, shorten <=-10pt,very thick,Stealth-Stealth}, grid=both, %major, major grid style={line width=1pt,draw=black!70}, minor x tick num=4, minor y tick num=4, ylabel = $y$, xlabel = $x$, width=3in, height=3in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, axis on top=false, axis line style = thick, major tick style = thick, xtick distance = 1, xlabel style={at={(ticklabel* cs:1.05)},anchor=west}, x grid style={thin, opacity=0.5}, ytick distance = 1, ylabel style={at={(ticklabel* cs:1.05)},anchor=south}, y grid style={thin, opacity=0.5}, axis on top=false, xtick={-4,-3,-2,-1,0,1,2,...,4}, ytick={-4,-3,-2,-1,0,1,2,...,6}, nodes near coords style={ above right=3pt, inner sep=0, color=black, font=,}, ] \addplot[name path=a, ultra thick, latex-latex, samples=300, smooth, domain=-1:2.5, red] {-2*\x+3} node [pos=0.9, left, red, font=\small] {}; \end{axis} \end{tikzpicture} \end{center} \end{multicols}

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Videos

Videos relating to Graphing Linear Equations.

  • Graphing Linear Equations - Video - Graph a Linear Equation Using a Table of Values

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