Question 1: Given the point (3, 4) and a gradient m = 2, write the equation of the line using y - y₁ = m(x - x₁).

Answer: y - 4 = 2(x - 3)

Question 2: Calculate the equation of the line passing through (1, -2) with a gradient of -3.

Answer: y + 2 = -3(x - 1)

Question 3: Determine the equation of the line that passes through (0, 5) with a gradient of 0.5.

Answer: y - 5 = 0.5(x - 0)

Question 4: Construct the equation of a line passing through (-2, 3) with gradient m = 4.

Answer: y - 3 = 4(x + 2)

Question 5: Find the equation of the line that passes through (2, -3) and has a gradient of 0.

Answer: y + 3 = 0(x - 2)

Question 6: A line passes through the points (1, 2) and (3, 6). Use y - y₁ = m(x - x₁) to find its equation.

Answer: First find m = (6 - 2)/(3 - 1) = 2. Using point (1, 2): y - 2 = 2(x - 1).

Question 7: A line passes through (4, -1) with a gradient of -0.5. Write its equation.

Answer: y + 1 = -0.5(x - 4)

Question 8: Using y - y₁ = m(x - x₁), derive the equation of the line passing through (0, 0) with m = 3.

Answer: y - 0 = 3(x - 0) or y = 3x

Question 9: A line has the equation y - 1 = 0.5(x - 2). Find its gradient and verify the point (2, 1) lies on it.

Answer: Gradient m = 0.5. Substituting x=2: y - 1 = 0.5(0) = 0, so y = 1, point lies on the line.

Question 10: An error is made when writing the equation y - 5 = -2(x + 1). Identify and correct the mistake if the point (1, 3) is on the line.

Answer: Incorrect: check if point (1, 3) satisfies the equation. Plug in x=1: y - 5 = -2(2) = -4, so y = 1, which is not 3. Correct equation: y - 5 = -2(x - 1).