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A student believes there is a correlation between the number of texts sent during class and GPA. The student collected data and found that the line of fit can be modeled by the equation [tex]\rho = 3.9 - 0.1x[/tex].

Identify and interpret the slope in this scenario.

A. The slope is 3.9. Starting at 0.1, the GPA will increase by 3.9 for every text sent in class.
B. The slope is 3.9. Starting at 0.1, the GPA will decrease by 3.9 for every text sent in class.
C. The slope is -0.1. Starting at 3.9, the GPA will increase by 0.1 for every text sent in class.
D. The slope is -0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.

Sagot :

GinnyAnswer
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."
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