We plot the graph having temperature in `""^(@)C` on x - axis and in `""^(@)F` on y - axis. If the graph is straight line, then the correct statement is

Options

A. the line intercepts the positive x - axis
B. the line intercepts the positive y - axis
C. the line passes through origin
D. the line intercepts the negative axis of both x and y - axes

Answer

To solve the problem of determining the correct statement about the graph of temperature in degrees Celsius plotted on the x-axis and temperature in degrees Fahrenheit plotted on the y-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between Celsius (C) and Fahrenheit (F) is given by the formula:
\[ F = 1.8C + 32 \]
This equation indicates how Fahrenheit changes with Celsius.

2. **Identify the Variables**:
In this equation, we can identify:
- \( y = F \) (temperature in Fahrenheit)
- \( x = C \) (temperature in Celsius)

3. **Rewrite the Equation**:
The equation can be rearranged to fit the slope-intercept form of a linear equation, \( y = mx + c \):
\[ F = 1.8C + 32 \]
Here, \( m = 1.8 \) (the slope) and \( c = 32 \) (the y-intercept).

4. **Graph Characteristics**:
- The slope (1.8) is positive, indicating that as Celsius increases, Fahrenheit also increases.
- The y-intercept (32) indicates that when Celsius is 0, Fahrenheit is 32.

5. **Determine Intercepts**:
- The graph will intersect the y-axis at \( F = 32 \) when \( C = 0 \).
- The graph will not pass through the origin (0,0) since when \( C = 0 \), \( F \) is not 0 but 32.

6. **Analyze the Options**:
Based on the graph characteristics:
- The line intercepts the positive y-axis (at \( F = 32 \)).
- The line does not intercept the positive x-axis (it does not pass through the origin).
- The line does not intercept the negative axes.

7. **Conclusion**:
The only correct statement is that the line intercepts the positive y-axis.

### Final Answer:
The correct statement is that the line intercepts the positive y-axis.

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