Question 1: Find the gradient of the line represented by the equation y=3x+5.

Answer: 3

Question 2: Write the equation of a line parallel to y=2x-4 that passes through the point (3,7).

Answer: y=2x+1

Question 3: Determine whether the lines y=4x+2 and y=-0.25x+5 are parallel. Justify your answer.

Answer: Yes, both have the same gradient magnitude (4 and -0.25 are not equal), so they are not parallel. No, they are not parallel.

Question 4: Construct a line on the grid that has the same gradient as the line passing through (0,0) and (4,8).

Answer: Line with equation y=2x

Question 5: Two lines have equations y=5x-1 and y=5x+3. Are these lines parallel? Explain your reasoning.

Answer: Yes, both lines have the same gradient of 5, so they are parallel.

Question 6: Plot the graph of y=2x and y=-2x on the grid. Do these lines have the same gradient? Explain.

Answer: No, their gradients are 2 and -2 respectively, so they are not parallel.

Question 7: Calculate the gradient of the line passing through points (1,2) and (3,6).

Answer: 2

Question 8: A line has the equation y=−3x+4. Find the equation of a line parallel to it passing through (2,1).

Answer: y=−3x+7

Question 9: Identify and correct the mistake: Line A has a gradient of 4, and Line B has a gradient of -4. Are these lines parallel? Why or why not?

Answer: No, because gradients are not equal; they are negatives. Parallel lines must have identical gradients, so they are not parallel.

Question 10: Challenge: The line y=−x+3 is transformed to y=−x−2 by shifting. Does the new line have the same gradient? Why?

Answer: Yes, the gradient remains −1; shifting does not change the gradient.