Answer
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.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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