https://file.aiquickdraw.com/mathbot/file/1726011213274s62qb2c8.jpg

The graph shows a linear relationship between the variables \( X \) and \( Y \). The line has a positive slope, as \( Y \) increases as \( X \) increases.

Now, let's evaluate the statements about the slope:

a. **The slope is positive until \( X = 4 \) and then negative**:  
   This is incorrect. The slope is positive throughout the entire graph, not just until \( X = 4 \).

b. **The slope is negative until \( X = 4 \) and then positive**:  
   This is incorrect. The slope is positive throughout the entire graph, so it is never negative.

c. **The slope is always positive and constant**:  
   This is correct. The graph shows a straight line, indicating a constant positive slope.

d. **The slope is always positive and increasing as \( X \) increases**:  
   This is incorrect. While the slope is positive, it is constant, not increasing. The slope of a straight line does not change.

**Correct answer: c. The slope is always positive and constant.**

Would you like further clarification or details?

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Here are 5 related questions to expand your understanding:

1. What is the slope of the line in this graph?
2. How do you calculate the slope of a straight line from two points on the graph?
3. What is the difference between positive, negative, zero, and undefined slopes?
4. How would the graph look if the slope were negative?
5. How does the slope of a line relate to the rate of change in real-world situations?

**Tip**: The slope of a line is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

The graphs below represent the relationship between two physical quantities X and Y. Which of the following statements about the slope of this graph is true?

Analyze the slope of a linear graph, where the relationship between X and Y is depicted. The slope remains positive and constant throughout, suitable for students in Grades 8-10 studying linear equations and graph analysis.

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