Graph the equation \( y=\frac{3}{5} x-6 \)

Certainly! Let's graph the linear equation: \[ y = \frac{3}{5}x - 6 \] ### Steps to Graph the Equation: 1. **Identify the Slope and Y-Intercept:** - **Slope (m):** \(\frac{3}{5}\) - **Y-Intercept (b):** \(-6\) 2. **Plot the Y-Intercept:** - Start by plotting the point where the line crosses the y-axis. This occurs at \((0, -6)\). 3. **Use the Slope to Find Another Point:** - The slope \(\frac{3}{5}\) means that for every 5 units you move horizontally (to the right), you move up 3 units vertically. - Starting from \((0, -6)\): - Move **right 5 units** to \(x = 5\). - Move **up 3 units** to \(y = -6 + 3 = -3\). - Plot the second point at \((5, -3)\). 4. **Draw the Line:** - Connect the two points with a straight line. - Extend the line in both directions and add arrowheads to indicate it continues indefinitely. ### Visual Representation: While I can't provide a graphical image, here's a simple **ASCII art** representation of the graph: ``` y | | | * | * | * | * |--------------------------- x (0, -6) (5, -3) ``` - The point at \((0, -6)\) is the y-intercept. - The point at \((5, -3)\) is the second point derived from the slope. - The asterisks (*) represent points on the line. ### Key Features of the Graph: - **Slope (\(m = \frac{3}{5}\)):** Indicates that the line rises 3 units for every 5 units it moves to the right. - **Y-Intercept (\(b = -6\)):** The line crosses the y-axis at \(-6\). ### Additional Points (Optional): To ensure accuracy, you can plot more points by choosing different \(x\)-values: - **For \(x = 10\):** \[ y = \frac{3}{5}(10) - 6 = 6 - 6 = 0 \] Point: \((10, 0)\) - **For \(x = -5\):** \[ y = \frac{3}{5}(-5) - 6 = -3 - 6 = -9 \] Point: \((-5, -9)\) Plotting these points will help confirm the straight-line nature of the graph. ### Summary: The graph of \( y = \frac{3}{5}x - 6 \) is a straight line with: - **Slope:** Rising gently as it moves to the right. - **Y-Intercept:** Crossing the y-axis at \(-6\). Feel free to use graphing paper or a graphing tool (like Desmos or GeoGebra) to visualize the equation more accurately!