Question 1: Plot the following data points on the grid: (1,2), (2,4), (3,6), (4,8).

Answer: Points plotted at coordinates (1,2), (2,4), (3,6), (4,8).

Question 2: Draw the line of best fit that approximately passes through the data points provided.

Answer: A straight line roughly passing through the middle of the points, extending across the grid.

Question 3: Given the points (1,1), (2,3), (3,5), (4,7), draw the line of best fit. Explain why this line is appropriate.

Answer: The line y=2x fits well, as the points roughly align along this line, indicating a strong positive linear relationship.

Question 4: Construct a line of best fit for the points: (1,5), (2,3), (3,4), (4,2).

Answer: A line with a negative slope, roughly passing through the middle of the data points, such as y = -0.5x + 5.

Question 5: Plot data points: (1,2), (2,4), (3,1), (4,3). Draw the line of best fit and describe its general trend.

Answer: The points suggest a slight negative trend; the line slopes downward overall.

Question 6: Using the plotted data, estimate the line of best fit and state its equation.

Answer: Approximate line y = -0.3x + 3.5 fits the data reasonably well.

Question 7: A set of data points shows a clear linear relationship. Draw the line of best fit and justify your choice.

Answer: The line y=1.5x + 0.5 passes through the middle of the points, capturing the trend effectively.

Question 8: Identify the common mistake made when drawing a line of best fit through scattered data points and explain how to correct it.

Answer: A common mistake is to draw a line simply connecting the outermost points. To correct it, the line should pass roughly through the center of the data, minimizing the sum of distances to all points.

Question 9: Given the points (1,3), (2,5), (3,4), (4,6), draw the line of best fit. Is the trend positive or negative?

Answer: Positive trend; the line slopes upward as x increases.

Question 10: Challenge: For the data points (1,2), (2,4), (3,6), (4,8), draw the line of best fit. Then, use the line to predict the value of y when x=5.

Answer: Line y=2x; when x=5, y=10.

Question 11: In a real-world scenario, students collected data on hours studied (x) vs. test scores (y). They plotted the data and drew a line of best fit. Describe how this line can help in predicting future test scores.

Answer: The line estimates the average test score for any given number of study hours, allowing students to predict their performance and plan accordingly.

Question 12: Error Analysis: A student draws a line that passes through only the highest and lowest data points, ignoring the others. Explain why this is incorrect and how to improve their drawing.

Answer: This approach misrepresents the overall trend. The line should balance the data points, passing roughly through the center, minimizing the total distance to all points.