Answer
To graph the equation \( y = \frac{3}{5}x - 6 \), plot the y-intercept at \((0, -6)\) and use the slope \(\frac{3}{5}\) to find another point, such as \((5, -3)\). Draw a straight line through these points to represent the equation.
Solution
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!
Reviewed and approved by the UpStudy tutoring team
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