The species - area relationship represented by the equation log s = log c + z log A is graphically seen as

Options

A. rectangular hyperbola with Z as its slope
B. straight line with Z as its slope
C. rectangular hyperbola with C as its slope
D. straight line with C as its slope

Answer

To solve the question regarding the species-area relationship represented by the equation \( \log S = \log C + z \log A \), we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation \( \log S = \log C + z \log A \) describes the relationship between species richness (S) and area (A). Here, \( C \) is a constant, and \( z \) is the slope of the line.

2. **Identifying Variables**:
- \( S \): Species richness (the number of different species in a given area).
- \( A \): Area (the size of the habitat).
- \( C \): A constant that relates to the specific characteristics of the area.
- \( z \): The slope of the line, indicating how species richness changes with area.

3. **Graphing the Equation**:
- On a graph, plot \( \log S \) on the Y-axis and \( \log A \) on the X-axis.
- According to the equation, this will yield a straight line because it is in the form of \( y = mx + b \) where \( y = \log S \), \( m = z \), \( x = \log A \), and \( b = \log C \).

4. **Interpreting the Slope**:
- The slope \( z \) indicates the rate at which species richness increases as the area increases. A positive value of \( z \) means that as the area increases, the number of species also increases.

5. **Conclusion**:
- The species-area relationship graphically represents a straight line, with \( z \) as the slope. This indicates a direct proportionality between the logarithm of species richness and the logarithm of area.

### Final Answer:
The species-area relationship represented by the equation \( \log S = \log C + z \log A \) is graphically seen as a straight line, where \( z \) is the slope.

---