Question 1: Calculate the gradient of the line passing through points (2, 5) and (6, 9).

Answer: 1

Question 2: Determine the equation of a line with gradient 3 passing through the point (4, 7).

Answer: y=3x+ (-5)

Question 3: Plot the graph of y=2x + 1 on the grid.

Answer: Student draws the line with slope 2 and y-intercept 1

Question 4: Two lines are parallel and both have a gradient of 4. Line A passes through (1, 2). Write the equation of Line A.

Answer: y=4x-2

Question 5: Find the gradient of a line that passes through (3, 6) and (7, 14).

Answer: 2

Question 6: Construct a line with the same gradient as the line y= -2x + 5 but passing through (2, 3).

Answer: y= -2x+7

Question 7: A park has two pathways that are parallel. Pathway 1 has a gradient of 1/2, and passes through (0, 0). Write its equation.

Answer: y= 1/2 x

Question 8: A taxi driver notes that two routes from the same point have the same gradient. Route A is y= 3x + 2, and Route B passes through (4, 14). Find the equation of Route B.

Answer: y=3x+2

Question 9: Explain why lines with the same gradient are parallel, using the concept of slope.

Answer: Lines with the same slope (gradient) rise and run at the same rate, which means they never intersect and are therefore parallel.

Question 10: A railway track needs to run parallel to an existing track with equation y= -1/3 x + 4. Find the equation for a new parallel track passing through (2, 1).

Answer: y= -1/3 x+ 5

Question 11: Identify and correct the mistake in this statement: 'Lines with the same gradient always intersect at some point.'

Answer: Correct statement: Lines with the same gradient are parallel and do not intersect. The mistake is that they always intersect.