Graph the line. $$ y=-3 x $$

Sure! Let's graph the linear equation $$ y = -3x $$. Here's a step-by-step guide to help you visualize and plot the line. ### 1. Understand the Equation The equation $$ y = -3x $$ is in the slope-intercept form $$ y = mx + b $$, where: - **Slope (m)**: -3 - **Y-intercept (b)**: 0 ### 2. Plot the Y-Intercept Start by plotting the y-intercept on the graph. - **Y-intercept (0, 0)**: This is where the line crosses the y-axis. ### 3. Use the Slope to Find Another Point The slope $$ m = -3 $$ can be interpreted as "rise over run," which means: - **Rise (Δy)**: -3 - **Run (Δx)**: 1 From the y-intercept (0, 0): - **Move right (positive x-direction) by 1 unit** - **Move down (negative y-direction) by 3 units** This brings you to the point (1, -3). ### 4. Plot Additional Points (Optional) For greater accuracy, you can plot more points using different x-values. Here's a table of some points on the line: | **x** | **y = -3x** | |-------|-------------| | -2 | 6 | | -1 | 3 | | 0 | 0 | | 1 | -3 | | 2 | -6 | ### 5. Draw the Line Connect the plotted points with a straight line extending in both directions. Make sure to include arrows on both ends to indicate that the line continues infinitely. ### 6. Visual Representation Here's a simple **ASCII graph** to help visualize $$ y = -3x $$: ``` y | 6 | * 5 | 4 | 3 | * 2 | 1 | 0 |*--------- x -1 | -2 | -3 | * -4 | -5 | -6 | * | +----------------- ``` **Points Plotted:** - (-2, 6) - (-1, 3) - (0, 0) - (1, -3) - (2, -6) ### 7. Graph Using Graphing Tools For a more precise and visually appealing graph, you can use graphing tools such as: - **Online Graphing Calculators**: - [Desmos](https://www.desmos.com/calculator) - [GeoGebra](https://www.geogebra.org/graphing) - **Spreadsheet Software**: - Microsoft Excel - Google Sheets ### 8. Summary - **Slope**: The line slopes downward from left to right since the slope is negative. - **Y-Intercept**: The line crosses the origin (0,0). - **Direction**: As $$ x $$ increases, $$ y $$ decreases proportionally. By following these steps, you can accurately plot and understand the line represented by $$ y = -3x $$. To graph the line $$ y = -3x $$, plot the y-intercept at (0,0). Then, use the slope of -3 to find another point by moving 1 unit right and 3 units down to (1, -3). Draw a straight line through these points, extending in both directions.

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Premium

Home Question Bank Math Algebra

Question

Graph the line.

Ask by Mills Ayala. in the United States

Jan 31,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

To graph the line

, plot the y-intercept at (0,0). Then, use the slope of -3 to find another point by moving 1 unit right and 3 units down to (1, -3). Draw a straight line through these points, extending in both directions.

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Mind Expander

To graph the line

, start by plotting the y-intercept at (0,0) since there is no constant term added. Next, use the slope, which is -3. From the y-intercept, move down 3 units and right 1 unit to find another point at (1, -3). Connect these points to see a straight line that slopes downwards from left to right.

For a clearer understanding, check the values of

for different

values: when

; when

. These points help you visualize and reinforce the steep negative slope of the line as you chart them on your graph!

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