Responder
To graph the equation \( b = \frac{h}{2} \), plot points where the base \( b \) is half the height \( h \). For example, when \( h = 2 \), \( b = 1 \). Draw a straight line through these points to represent the relationship between the base and height of the triangle.
Solución
Certainly! Let's graph the equation \( b = \frac{h}{2} \), where:
- \( h \) represents the **height** of the triangle.
- \( b \) represents the **base** of the triangle.
### Understanding the Equation
The equation \( b = \frac{h}{2} \) shows a linear relationship between the base and the height of the triangle. For every unit increase in height, the base increases by half a unit.
### Steps to Graph \( b = \frac{h}{2} \)
1. **Choose a Coordinate System:**
- **Horizontal Axis (X-axis):** Base (\( b \))
- **Vertical Axis (Y-axis):** Height (\( h \))
2. **Create a Table of Values:**
| Height (\( h \)) | Base (\( b = \frac{h}{2} \)) |
|------------------|-------------------------------|
| 0 | 0 |
| 2 | 1 |
| 4 | 2 |
| 6 | 3 |
| 8 | 4 |
| 10 | 5 |
3. **Plot the Points:**
| \( b \) (Base) | \( h \) (Height) |
|----------------|------------------|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
4. **Draw the Line:**
- Connect the plotted points with a straight line.
- Extend the line in both directions for a complete graph.
### Visual Representation
Here's a simplified **ASCII** representation of the graph:
```
Height (h)
|
10 | *
9 |
8 | *
7 |
6 | *
5 |
4 | *
3 |
2 | *
1 |
0 |_______________________________ Base (b)
0 1 2 3 4 5
```
- Each `*` represents a plotted point from the table.
- The line connecting these points illustrates the relationship \( b = \frac{h}{2} \).
### Graph Interpretation
- **Slope:** The slope of the line is \( \frac{1}{2} \), indicating that for every increase of 2 units in height, the base increases by 1 unit.
- **Intercept:** The graph passes through the origin (0,0), meaning when the height is 0, the base is also 0.
### Practical Example
Suppose you have a triangle with a height of 6 units:
\[ b = \frac{6}{2} = 3 \text{ units} \]
On the graph, this corresponds to the point (3, 6), which lies on the line \( b = \frac{h}{2} \).
### Using Graphing Tools
For a more precise graph, you can use graphing tools or software such as:
- **Desmos:** [https://www.desmos.com/calculator](https://www.desmos.com/calculator)
- **GeoGebra:** [https://www.geogebra.org/graphing](https://www.geogebra.org/graphing)
- **Microsoft Excel or Google Sheets:** Utilize their charting features to plot the points and draw the line.
### Conclusion
Graphing \( b = \frac{h}{2} \) provides a clear visual representation of how the base and height of Bodie's triangle are related. By understanding this relationship, you can easily determine one dimension when the other is known.
Revisado y aprobado por el equipo de tutoría de UpStudy
Explicar
Simplifique esta solución
