Question 1: Calculate the gradient of the line passing through points (2, 3) and (5, 9).

Answer: 2

Question 2: Find the gradient of the line given by the equation 3x - 2y = 6.

Answer: 3/2

Question 3: Two lines have gradients 4 and 4/3. Are these lines parallel? Explain your answer.

Answer: No, because the gradients are not equal.

Question 4: Construct a line passing through (1, 2) with the same gradient as the line passing through (0, 0) and (4, 8).

Answer: y=2x + c (any line with gradient 2)

Question 5: Determine whether the line passing through (3, 5) and (6, 11) is parallel to the line y=2x + 1.

Answer: Yes, because both have gradient 2.

Question 6: Find the gradient of the line that passes through points (-1, 4) and (2, -2).

Answer: -2

Question 7: A line has a gradient of 3. Write an equation of a line with this gradient passing through the point (2, 5).

Answer: y=3x - 1

Question 8: Identify the mistake in this statement: 'Two lines are parallel because they have different gradients.'

Answer: The statement is incorrect because parallel lines have the same gradient.

Question 9: Construct two lines on the grid that are parallel and pass through the points (1, 1) and (4, 4), and (2, 3) and (5, 6).

Answer: Both lines have gradient 1

Question 10: Explain why two lines with the same gradient but different y-intercepts are parallel.

Answer: Because having the same gradient means they have the same slope, so they are parallel even if their y-intercepts differ.

Question 11: Find the gradient of the line passing through points (0, 0) and (2, 5).

Answer: 5/2