Question 1: Calculate the gradient of the line shown on the grid that is perfectly horizontal.

Answer: 0

Question 2: A line on a graph is horizontal. What is its gradient? Explain your answer.

Answer: The gradient is zero because the line has no rise over run; it is flat.

Question 3: Construct a straight line on the grid with a gradient of zero. Describe the key features of your line.

Answer: A horizontal line, where every point has the same y-coordinate.

Question 4: Identify the mistake in this reasoning: 'Since the line is horizontal, its gradient must be 1.'

Answer: The mistake is assuming the gradient is 1; a horizontal line has gradient 0.

Question 5: A graph shows a straight line with a gradient of zero. What does this tell you about the change in y-values along the line?

Answer: There is no change in y-values; y remains constant along the line.

Question 6: Plot the graph of y=5. What is the gradient of this line? Explain your reasoning.

Answer: Gradient is 0 because y=5 is a horizontal line.

Question 7: If a line has a gradient of zero, which types of lines can it be? Give two examples.

Answer: Any horizontal line, e.g., y=0 or y=−3.

Question 8: Common misconception: A horizontal line has an undefined gradient. Is this true? Why or why not?

Answer: No, it's false; a horizontal line has a gradient of 0, which is defined.

Question 9: A line on a graph is horizontal but appears to slope downward due to poor drawing. What mistake might students make when calculating the gradient?

Answer: They might measure a negative slope; the line is actually flat, so gradient is zero.

Question 10: A roller coaster track is flat at one section. How does this relate to the concept of zero gradient?

Answer: A flat section has zero gradient, meaning no change in height over distance, indicating a horizontal track.

Question 11: Identify and correct the error: 'Since the gradient of the line is zero, the line must be vertical.'

Answer: The mistake is assuming a zero gradient means vertical; actually, a vertical line has undefined gradient, not zero.