Question 1: Calculate the gradient of a line passing through points (2, 5) and (6, 1).

Answer: -1

Question 2: Determine the gradient of the line drawn on the grid that passes through points (-3, 4) and (1, 0).

Answer: -1

Question 3: Construct a line on the grid with a gradient of -0.5 passing through point (4, 2).

Answer: Line passes through (4, 2) with slope -0.5

Question 4: Plot the graph of y = -3x + 4 on the grid. Describe the gradient and how it relates to the line's steepness and direction.

Answer: Gradient is -3; the line slopes downward steeply from left to right.

Question 5: A line on the graph passes through (1, 3) and (4, -2). Calculate its gradient. Is it positive or negative?

Answer: -5, negative

Question 6: Explain why the gradient of a line that goes from (0, 0) to (0, 5) is undefined. What does this mean in terms of slope?

Answer: Because the change in x is zero, division by zero makes the gradient undefined; this means the line is vertical.

Question 7: Determine the gradient of the line with the equation y = -2x + 7.

Answer: -2

Question 8: A line passes through points (-1, -3) and (2, 4). Calculate the gradient and describe its sign.

Answer: 2.33, positive

Question 9: A line has a gradient of -4. If it passes through (3, 2), find the equation of the line.

Answer: y = -4x + 14

Question 10: Identify and correct the mistake: A student calculates the gradient between points (1, 2) and (1, 5) as 3.

Answer: Incorrect because the change in x is zero; the correct gradient is undefined (vertical line).

Question 11: Compare the gradients of the lines passing through (0, 0) and (5, -5), and through (0, 0) and (-4, 8). Which line has a steeper negative slope?

Answer: Both have slope -1; equal in steepness.