\begin{tabular}{l} Graph the linear equation. \\ \( 3 x+y=9 \) \\ Use the graphing tool to graph the linear equation. \\ \hline \( \begin{array}{l}\text { Click to } \\ \text { enlarge } \\ \text { graph }\end{array} \) \\ \hline\end{tabular}

To graph the linear equation \(3x + y = 9\), you can start by rewriting it in slope-intercept form: \(y = -3x + 9\). This tells you the slope of the line is -3, which means for every 1 unit you move to the right along the x-axis, you'll move down 3 units on the y-axis. The y-intercept of this line is at (0, 9), where the line crosses the y-axis. Now for real-world application: imagine you're budgeting your monthly expenses. If \(x\) represents the number of luxury items you buy (let's say each costs $3), and \(y\) represents the money you have left, the equation shows that once you’ve spent on luxury items, there’s a set amount you'll have left to spend — namely, $9! Graphing this helps visualize how your spending affects your savings.