Resources for Intersecting Lines
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Intersecting Lines Theory
![\textbf{Example}\\ The graphs of \(y=x+2\) and \(y=-2 x-1\) are given on the number plane.\\ \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,...,8}, 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=-2:1, red] {-2*\x-1} node [pos=0.9, left, red, font=\small] {}; \addplot[name path=b, ultra thick, latex-latex, samples=300, smooth, domain=-3:1, blue] {\x+2} node [pos=0.9, left, red, font=\small] {}; \addplot[black, mark=*] coordinates {(-1,1)}; \end{axis} \end{tikzpicture} \end{center} \hfill\linebreak \textbf{i)} Use the graphs to solve the equation \(x+2=-2 x-1\)\\ \textbf{ii)} Find the coordinates of the point where the line \(y=-2 x-1\) cuts the \(y\)-axis\\ \textbf{iii)} Find the coordinates of the point where the line \(y=x+2\) cuts the \(x\)-axis\\ \textbf{Example solution}\\ \textbf{i)} From the graph the point of intersection is \((-1,1)\)\qquad \(\therefore x=-1\)\\ \textbf{ii)} From the graph \(y=-2 x-1\) cuts the \(y\)-axis at \((0,-1)\)\\ \textbf{iii)} From the graph \(y=x+2\) cuts the \(x\)-axis at \((-2,0)\)](/media/vo1j0krp/9867.png)
NSW Y8 Maths Graphing Linear Equations Intersecting Lines
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Intersecting Lines - Video - How to find the point of intersection of two straight lines by graphing
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