Write a function rule for "The output is one-third of the input \( x \)." \[ y=\square \] Graph the function. Line Undo Redo Reset

Certainly! Let's break down your request into two parts: writing the function rule and graphing the function. --- ## 1. Function Rule **Statement:** "The output is one-third of the input \( x \)." **Function Rule:** \[ y = \frac{1}{3}x \] This equation means that for every value of \( x \), the corresponding value of \( y \) is one-third of \( x \). --- ## 2. Graph of the Function \( y = \frac{1}{3}x \) ### Description - **Slope (Rise over Run):** The coefficient of \( x \) is \( \frac{1}{3} \), which means the line rises 1 unit vertically for every 3 units it moves horizontally. - **Y-Intercept:** The line passes through the origin (0,0), so the y-intercept is 0. ### Graphical Representation While I can't provide a visual graph here, I can describe how to plot it or present a simple ASCII representation. #### Plotting the Graph 1. **Choose Values for \( x \):** Select a few values for \( x \) to find corresponding \( y \) values. | \( x \) | \( y = \frac{1}{3}x \) | |---------|------------------------| | -3 | -1 | | 0 | 0 | | 3 | 1 | | 6 | 2 | | 9 | 3 | 2. **Plot the Points:** Plot the points \((-3, -1)\), \((0, 0)\), \((3, 1)\), \((6, 2)\), and \((9, 3)\) on a coordinate plane. 3. **Draw the Line:** Connect the points with a straight line extending in both directions. #### Simple ASCII Graph ``` y | 3 | * 2 | * 1 | * 0 |*------------------------- x -1| -2| -3| ``` *Each "*" represents a plotted point. Connect them to form a straight line.* ### Using Graphing Tools For a more accurate and visually appealing graph, you can use online graphing calculators such as: - **[Desmos](https://www.desmos.com/calculator):** Enter the equation \( y = \frac{1}{3}x \) to see the graph. - **[GeoGebra](https://www.geogebra.org/graphing):** Another powerful tool for plotting and analyzing functions. --- ## Additional Controls It seems you mentioned some interface controls like **Line**, **Undo**, **Redo**, and **Reset**. These are typically used in graphing software or interactive math platforms. Here's a brief overview of how they might function: - **Line:** Selects the tool to draw a straight line, useful for plotting linear functions. - **Undo:** Reverses the last action, allowing you to correct mistakes. - **Redo:** Re-applies an action that was undone. - **Reset:** Clears the current graph or resets settings to default. If you're using a specific platform or tool, these controls will help you manipulate the graph as needed. --- Feel free to ask if you need further assistance with graphing or understanding the function!