To address the student's question about the correlation between the number of texts sent during class and GPA, let's carefully examine the given equation [tex]\(\rho = 3.9 - 0.1x\)[/tex].
In this equation:
- [tex]\(\rho\)[/tex] stands for the GPA.
- [tex]\(x\)[/tex] represents the number of texts sent during class.
- The term [tex]\(3.9\)[/tex] is the y-intercept, which is the GPA when no texts are sent.
- The term [tex]\(-0.1\)[/tex] is the slope, which indicates the change in GPA for each additional text sent during class.
Step-by-Step Explanation:
1. Identify the Slope and Intercept:
- The slope (represented as [tex]\(m\)[/tex] in linear equations) is [tex]\(-0.1\)[/tex].
- The y-intercept is [tex]\(3.9\)[/tex].
2. Interpret the Slope:
- The slope of [tex]\(-0.1\)[/tex] means that for every additional text sent during class, the GPA decreases by [tex]\(0.1\)[/tex].
- A negative slope indicates a negative relationship between the number of texts sent and the GPA; as one increases, the other decreases.
3. Interpret the Full Equation:
- When no texts are sent ([tex]\(x = 0\)[/tex]), the GPA ([tex]\(\rho\)[/tex]) starts at [tex]\(3.9\)[/tex].
- For each additional text sent ([tex]\(x\)[/tex] increases by 1), the GPA ([tex]\(\rho\)[/tex]) decreases by [tex]\(0.1\)[/tex].
Conclusion:
Given the correct slope and interpretation:
The slope is [tex]\(-0.1\)[/tex]. Starting at [tex]\(3.9\)[/tex], the GPA will decrease by [tex]\(0.1\)[/tex] for every text sent in class.
Therefore, the correct answer is:
"The slope is [tex]\(-0.1\)[/tex]. Starting at [tex]\(3.9\)[/tex], the GPA will decrease by [tex]\(0.1\)[/tex] for every text sent in class."
