To solve the problem shown in the scatter plot:

(a) Writing an Approximate Line of Best Fit

From the scatter plot:

• The data appears to be roughly linear, showing a positive trend.
• Estimating the slope ($m$) and y-intercept ($b$):
  • For approximate calculations, we pick two points: (20, 30) and (80, 90).
  • Slope: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{90 - 30}{80 - 20} = \frac{60}{60} = 1$
  • Using one point, say (20, 30), to find $b$ using the line equation $y = mx + b$: $30 = 1(20) + b \implies b = 30 - 20 = 10$

The approximate equation of the line of best fit is: $\hat{y} = 1x + 10$

(b) Predicting Quiz Score for 50 Minutes

Substitute $x = 50$ into the equation: $\hat{y} = 1(50) + 10 = 50 + 10 = 60$

Final Answers:

(a) The equation of the line of best fit is: $\hat{y} = 1x + 10$

(b) The predicted quiz score for 50 minutes of studying is: $60$

Would you like a detailed step-by-step explanation or to verify a specific part of the calculation?

Related Questions:

1. How can we calculate the slope more precisely if provided with exact data points?
2. How do outliers affect the line of best fit in scatter plots?
3. Can we solve this problem using software tools like Excel or graphing calculators?
4. How can the correlation coefficient (r) help us understand the data's linearity?
5. What does the y-intercept represent in this context?

Tip: Always ensure that the chosen points for estimating the slope are well-distributed and representative of the overall trend.