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

Answer: −1

Question 2: Plot the graph of y = -2x + 3. Describe the gradient of the line.

Answer: The gradient is -2, which is negative.

Question 3: Construct a line on the grid that has a gradient of -3. Use any two points you like.

Answer: Any two points with difference in y = -3 times the difference in x, e.g., (1, 2) and (3, -4).

Question 4: A line passes through (0, 4) and (4, 0). Calculate its gradient and determine whether it is positive or negative.

Answer: −1

Question 5: A graph shows a line decreasing from left to right. If the line goes through (1, 3) and (4, 0), what is its gradient?

Answer: −1

Question 6: Explain why the gradient of a line that slopes downward from left to right is always negative.

Answer: Because as x increases, y decreases, resulting in a negative change in y over change in x.

Question 7: A real-world example: A car descends a hill, and its height drops from 150 meters to 100 meters over a horizontal distance of 500 meters. Calculate the gradient of the slope.

Answer: −0.1

Question 8: Construct a line with a gradient of -2 passing through the point (2, 5). Write down the equation of the line.

Answer: y = -2x + 9

Question 9: A line has a gradient of -1.5 and passes through the point (4, 2). Find the equation of the line.

Answer: y = -1.5x + 8

Question 10: Identify and correct the mistake: A student states that a line with points (1, 2) and (3, 6) has a negative gradient.

Answer: Incorrect; the gradient is (6−2)/(3−1) = 4/2 = 2, which is positive.

Question 11: Challenge: Find the equation of a line with a negative gradient of -0.5 that crosses the y-axis at y=4. Plot this line on the grid.

Answer: y = -0.5x + 4