The equation of the trend line you've provided, \( y = -7.2x + 98.9 \), shows a linear relationship between the number of hours spent on social media (represented by \( x \)) and the average final grade (represented by \( y \)).
Interpretation of the Equation:
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Slope (\(-7.2\)):
- The slope of the line is \(-7.2\), which indicates that for every additional hour spent on social media, the average final grade decreases by 7.2 points. This suggests that increased social media use is associated with lower grades.
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Y-intercept (\(98.9\)):
- The y-intercept of the equation is \(98.9\). This means that if a student were to spend \(0\) hours on social media, their expected average final grade would be \(98.9\).
Implications:
- The negative slope suggests a potentially adverse impact of social media usage on academic performance. The more time students spend on social media, the lower their grades may be.
Example Calculation:
If you want to find out the expected average final grade for a student who spends, for example, \(4\) hours on social media, you can substitute \(x = 4\) into the equation:
\[ y = -7.2(4) + 98.9 \] \[ y = -28.8 + 98.9 \] \[ y = 70.1 \]
So, a student who spends \(4\) hours on social media would be expected to have an average final grade of \(70.1\).
This information can help guide students to be mindful of their social media habits in relation to their academic performance.