Question 1: Plot the points (1, 2), (2, 4), (3, 6), and (4, 8) on the grid. Draw a line of best fit through these points.

Answer: Line passing approximately through (0, 0) and (5, 10)

Question 2: Construct a scatter plot with the following data: (1, 3), (2, 5), (3, 7), (4, 9). Draw the line of best fit.

Answer: Line roughly passing through (0, 1.5) and (5, 10)

Question 3: Given the points (2, 4), (3, 7), (4, 10), draw the scatter plot and sketch the line of best fit.

Answer: Line approximately passing through (1, 1) and (5, 13)

Question 4: On a scatter plot, points seem to lie roughly along a straight line. Explain the key features to consider when drawing the line of best fit.

Answer: Consider the overall trend of the points, minimizing the distance from all points, balancing above and below points.

Question 5: Draw a line of best fit for the following data: (1, 2), (2, 3), (3, 3), (4, 4). Use the grid to sketch your line.

Answer: Line roughly passing through (1, 2.2) and (4, 3.8)

Question 6: For the data points (1, 1), (2, 2), (3, 3), (4, 4), draw the scatter plot and sketch the line of best fit.

Answer: Line along y = x

Question 7: Identify and correct the mistake in the following student's drawing: The line of best fit passes through (0, 0) but is very steep, crossing points at high y-values.

Answer: The line is too steep; it does not reflect the overall trend. The line should be more moderate, closer to the middle of the points.

Question 8: Plot these points: (1, 5), (2, 7), (3, 6), (4, 8). Draw the line of best fit. How does the line help predict y-values for x = 5?

Answer: The line can be extended beyond x=4 to approximate y at x=5, likely around y=9 based on the trend.

Question 9: Construct a scatter plot with points (2, 2), (4, 4), (6, 6), (8, 8). Draw the line of best fit.

Answer: Line along y = x, passing through all points

Question 10: Using the grid, draw a scatter plot with points (1, 3), (2, 6), (3, 9), (4, 12). Sketch the line of best fit.

Answer: Line approximately passing through (0, 0) and (5, 15)

Question 11: Evaluate why the line of best fit may not pass through all points on a scatter plot, even if some points lie exactly on the line.

Answer: Because the line minimizes the overall distance to all points, it may not pass through every point but best represents the trend.