Question 1: Plot the points (2, 3), (4, 5), and (6, 7) on the grid. Draw the line of best fit passing through these points.

Answer: Line passing through the points, roughly y = x + 1

Question 2: Using the data points (1, 2), (3, 4), (5, 6), calculate the approximate gradient of the line of best fit.

Answer: 1

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

Answer: A diagonal line passing through the points, y = x

Question 1: A student collects data on hours studied versus test scores. The points roughly follow a linear trend. Describe how you would draw a line of best fit, and explain what this line indicates about the data.

Answer: Plot the points, then draw a straight line that best represents the overall trend, minimizing deviations. The line indicates the average test score for a given study time.

Question 2: Given the points (2, 5), (4, 9), and (6, 13), draw the line of best fit. Estimate the y-value when x = 8.

Answer: Approximately 17

Question 1: A bakery tracks the number of cakes sold each day over a week: 10, 12, 14, 16, 18, 20, 22. Plot the data and draw the line of best fit to predict sales for the next day.

Answer: A line going through the points, predicting around 24 cakes sold on the eighth day.

Question 2: A sports coach records the distance run by athletes in seconds: 50, 45, 40, 35, 30. Draw the points and sketch a line of best fit to analyze the trend.

Answer: A downward trend line, estimating upcoming run times.

Question 1: Given points (1, 2), (3, 6), and (5, 10), draw the line of best fit. Using this line, predict the y-value when x=7.

Answer: Approximately 14

Question 2: Identify and correct the mistake if a student draws a line that connects the first and last points only, ignoring the middle point. Explain why this is incorrect.

Answer: This is incorrect because the line would not accurately represent the overall trend; a line of best fit minimizes the overall deviation.

Question 1: Plot these points: (1, 4), (2, 5), (3, 7). Draw the line of best fit.

Answer: Line roughly passing through the points, with a positive slope.

Question 2: Construct a line of best fit for the data points: (0, 1), (2, 3), (4, 5).

Answer: Y = x + 1

Question 1: A student draws a line that connects only the outermost data points, ignoring the middle points. Why is this incorrect? How should they improve?

Answer: Connecting only the outermost points does not minimize the overall distances; the line should be drawn to best fit all points collectively, not just extremes.