Question 1: Find the equation of a line with a gradient of 3 passing through the point (2, 5).

Answer: y = 3x - 1

Question 2: A line is parallel to the line y = -2x + 4 and passes through the point (1, -3). Write its equation.

Answer: y = -2x - 1

Question 3: Construct the equation of a line with a gradient of 0.5 and y-intercept at 2.

Answer: y=0.5x+2

Question 4: A line has the equation y = 4x + 3. Find the equation of a line perpendicular to it passing through (0, 1).

Answer: y = -0.25x + 1

Question 5: Identify and correct the mistake in the following line equation: y = 2x + 5, given the line passes through (1, 7) with a gradient of 2.

Answer: Incorrect; using point (1,7) and gradient 2, the correct equation is y=2x+5 (no mistake).

Question 6: A student claims the line y = -x + 4 is parallel to y = -x + 7. Is this correct? Explain your reasoning.

Answer: Yes, both lines have the same gradient (-1), so they are parallel.

Question 7: Using the point (3, 2) and gradient 0.75, write the equation of the line.

Answer: y=0.75x - 0.25

Question 8: Derive the equation of a line perpendicular to y = 5x - 2 and passing through (4, 1).

Answer: y = -0.2x + 1.8

Question 9: Plot the graph of y=2x on the grid provided. (Construct the line accordingly.)

Answer: Line plotted through (0,0), (1,2), etc.

Question 10: A line with equation y = -0.5x + 4 is moved parallel downward by 3 units. Write the new equation.

Answer: y=-0.5x + 1

Question 11: Identify the error in this student's work: They state the line passing through (2,3) with slope 2 is y=2x+1. (Work: y - 3 = 2(x - 2) → y - 3 = 2x - 4 → y=2x - 1).

Answer: Incorrect; the correct equation is y=2x - 1, but the student's working is correct, so the error is in the initial statement or interpretation. (Note: The student's work is correct; the mistake is in the question's assumption.)