Question 1: Given the data points, draw the line of best fit and use it to estimate the y-value when x = 10.

Answer: Estimate based on the drawn line

Question 2: Calculate the gradient of the line of best fit for the data points: (2, 4), (4, 8), (6, 12).

Answer: 2

Question 3: Explain how the line of best fit can be used to make predictions in a real-world scenario, such as estimating sales based on advertising spend.

Answer: Students should describe predicting sales using the line of best fit derived from historical data.

Question 4: Plot the graph of y = 3x + 2 on the grid. Use the line to predict y when x = 5.

Answer: 17

Question 5: The data shows a positive correlation between x and y. What does this suggest about the relationship between these variables?

Answer: As x increases, y tends to increase.

Question 6: A student drew a line of best fit but the predictions are consistently too high. What could be the reason?

Answer: The line might have a positive bias; perhaps outliers skewed the line upward.

Question 7: Using the data points (1, 2), (3, 6), (5, 10), find the equation of the line of best fit.

Answer: y = 2x

Question 8: A scatter plot with a line of best fit is drawn. The data points are tightly clustered around the line. What does this indicate about the prediction accuracy?

Answer: High accuracy; predictions are likely reliable.

Question 9: If the line of best fit predicts y = 4.5x + 1, what is the predicted y when x = 7?

Answer: 32.5

Question 10: Identify and explain a common mistake made when calculating the line of best fit from a small dataset.

Answer: Using a line that fits all points exactly, ignoring potential outliers; overfitting.

Question 11: Challenge: Given the data points (1, 3), (2, 5), (3, 7), and (4, 9), find the line of best fit and use it to predict y when x=6.

Answer: y = 2x + 1; prediction y=13