Question 1: Find the equation of a line that is parallel to y = 3x + 2 and passes through the point (4, 5).

Answer: y = 3x + 1

Question 2: Determine the equation of a line parallel to 2x - y = 4 that passes through the point (1, -2).

Answer: y = 2x - 4

Question 3: Calculate the gradient of the line y = - x + 7.

Answer: -

Question 4: Construct a line parallel to y = 4x - 3 that passes through the point (0, 2). Write its equation.

Answer: y = 4x + 2

Question 5: A line has the equation y = 2x + 5. Find the equation of a parallel line passing through the point (-1, 4).

Answer: y = 2x + 6

Question 6: A line passes through (2, 3) and is parallel to y = -2x + 1. Find its equation.

Answer: y = -2x + 7

Question 7: Plot the graph of y = 2x on the grid provided. Draw a line parallel to it passing through (1, 4).

Answer: y = 2x + 2

Question 8: Construct a triangle with vertices at (0,0), (2,4), and (4,0). Draw a line parallel to the base and passing through the midpoint of the hypotenuse. Write its equation.

Answer: y = -x + 2

Question 9: A line with equation y = -x + 3 is extended. Find the equation of a line parallel to it that passes through (3, -2).

Answer: y = -10x + 28

Question 10: Identify and correct the mistake in the following: The line y = 5x - 4 passes through (0, -4) but the student states its parallel line through (2, 6) is y = 5x + 4.

Answer: The parallel line should pass through (2, 6), so its equation is y = 5x + 4. The mistake is in the student's statement; actually, the correct parallel line is y = 5x + 4.