1. **State the problem:** We are given the regression line equation $$y = -\frac{2}{3}x + \frac{125}{3}$$ which estimates IB Diploma points ($y$) based on hours spent on social media ($x$). An eleventh girl spent 34 hours on social media, and we need to estimate her IB Diploma points using the regression line. 2. **Use the regression line formula:** The formula to estimate $y$ given $x$ is: $$y = -\frac{2}{3}x + \frac{125}{3}$$ 3. **Calculate the estimate for $x=34$:** Substitute $x=34$ into the equation: $$y = -\frac{2}{3} \times 34 + \frac{125}{3}$$ Calculate each term: $$-\frac{2}{3} \times 34 = -\frac{68}{3}$$ So, $$y = -\frac{68}{3} + \frac{125}{3} = \frac{125 - 68}{3} = \frac{57}{3} = 19$$ Therefore, the estimated IB Diploma points for the girl who spent 34 hours on social media is **19 points**. 4. **Reason why this estimate is not reliable:** The original data only includes students who spent between 3 and 30 hours on social media. The value $x=34$ is outside this range, so this estimate is an **extrapolation** beyond the observed data. Extrapolations can be unreliable because the linear relationship may not hold outside the observed range. **Final answer:** The estimated IB Diploma points for the girl who spent 34 hours on social media is **19 points**. This estimate is not reliable because it is an extrapolation beyond the data range (3 to 30 hours).