Resources for Finding the Rule
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Finding the Rule Theory
![\begin{multicols}{2} \textbf{Example 1} \begin{center} \begin{tabular}{|l|l|l|l|l|} \hline x & 0 & 1 & 2 & 3 \\ \hline y & 5 & 6 & 7 & 8 \\ \hline \end{tabular} \end{center} \hfill\linebreak \textbf{i)} \(y=x+b\) Find \(b\)\\ \begin{center} \begin{tabular}{|l|l|l|l|l|} \hline x & 0 & 1 & 2 & 3 \\ \hline y & 5 & 7 & 9 & 11 \\ \hline \end{tabular} \end{center} \hfill\linebreak \textbf{ii)} \(y=m x+5\) Find \(m\)\\ \textbf{Example 1 solution}\\ \textbf{i)} when \(x=0, y=5\)\\ \(\begin{aligned} 5&=0+b \\ \therefore b&=5 \\ \therefore y&=x+5 \end{aligned}\)\\[3pt] \textbf{ii)} when \(x=1, y=7\)\\ \(\begin{aligned} \therefore 7 & =m+5 \\ \therefore m & =2 \\ \therefore y & =2 x+5 \end{aligned}\) \columnbreak \textbf{Example 2} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline y & 6 & 4 & 2 & 0 \\ \hline \end{tabular} \end{center} \(y=m x+b\)\\ find \(m\) and \(b\).\\ \textbf{Example 2 solution}\\ when \(x=0, y=6\)\\ \(\begin{aligned} \therefore 6 & =0+b \\ b & =6 \end{aligned}\)\\ when \(x=1, y=4\)\\ \(\begin{aligned} \therefore 4&=m+6 \\ \therefore m&=-2 \end{aligned}\)\\ \(\begin{aligned} \therefore m&=-2 \text { and } b=6 \\ \therefore y&=-2 x+6 \end{aligned}\) \end{multicols}](/media/wsnhqsvz/9862.png)
NSW Y8 Maths Graphing Linear Equations Finding the Rule
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Finding the Rule - Video - Visual Pattern - Writing an Equation and Creating a Table
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