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

Answer: -1

Question 2: Find the gradient of the line with the equation y = -3x + 4.

Answer: -3

Question 3: Determine the gradient of a line passing through points (0, 0) and (4, -8).

Answer: -2

Question 4: Construct a line on the grid with a gradient of -1/2 passing through the point (2, 3).

Answer: Line passes through (2,3) and (4,2), for example.

Question 1: A car is moving down a hill, and its height (in meters) decreases as it travels along the road. The height y decreases at a rate of 4 meters for every 5 meters traveled along the road. What is the gradient of the slope of the hill?

Answer: -4/5

Question 2: Explain why a line with a negative gradient slopes downward from left to right. Use the concept of change in y and change in x in your answer.

Answer: A negative gradient means that as x increases, y decreases. This results in the line sloping downward from left to right because the change in y is negative while the change in x is positive.

Question 3: A line passes through points (1, 4) and (3, 0). Verify the gradient and explain if it is negative.

Answer: -2

Question 4: A graph shows a line with a negative slope. A student claims the gradient is positive. Identify and correct the mistake in their reasoning.

Answer: The mistake is in the student's interpretation. A negative slope means the line slopes downward from left to right, so the gradient must be negative, not positive.

Question 1: A cyclist descends a hill, losing 60 meters in height over a horizontal distance of 120 meters. What is the gradient of the hill? Is it positive or negative?

Answer: -0.5

Question 2: A road declines from point A to point B. If the elevation at A is 150 meters and at B is 90 meters over a distance of 30 km, what is the gradient? Is the slope negative?

Answer: -2/3

Question 1: Construct a line on the grid with a gradient of -3/4 passing through the origin. Describe the steps or coordinates you use.

Answer: Line passes through (0,0) and (4, -3).

Question 2: Given a line with a negative gradient, explain how the change in y relates to the change in x. Provide an example with specific points.

Answer: Since the gradient is negative, as x increases, y decreases. For example, between points (2, 5) and (4, 1), the change in y is -4 and change in x is 2, so gradient = -4/2 = -2.

Question 1: A student calculates the gradient between points (3, 7) and (1, 3) as 2. Is this correct? If not, what is the mistake and what should the correct gradient be?

Answer: Incorrect. The change in y is 4 (7-3), and change in x is -2 (1-3). Gradient = 4 / -2 = -2. The mistake was ignoring the negative change in x.

Question 2: A line appears to slope downward but the student reports its gradient as +3. What common misconception might this indicate?

Answer: The student may be confusing the visual slope with the numerical sign. Since the line slopes downward from left to right, the gradient must be negative, not positive.