Question 1: Calculate the gradient of a line passing through the points (2, 3) and (5, 6).

Answer: 1

Question 2: A line passes through (1, 2) and (4, 5). What is its gradient?

Answer: 1

Question 3: On a graph, a line rises from (0, 0) to (3, 3). Calculate the gradient.

Answer: 1

Question 4: Construct a line with a gradient of 2 passing through the point (1, 1).

Answer: y=2x

Question 5: Plot the graph of y=3x+1 and identify the gradient.

Answer: 3

Question 6: A line passes through (2, 4) and (6, 10). Is the gradient positive? Show your working.

Answer: Yes; (10-4)/(6-2)=6/4=1.5>0

Question 7: Explain why a line with a positive gradient slopes upward from left to right.

Answer: Because as x increases, y also increases, resulting in an upward slope.

Question 8: A graph shows a line rising from (0, 1) to (4, 5). Calculate the gradient and interpret its meaning in this context.

Answer: 1; the y-value increases by 1 for every 1 increase in x

Question 9: Identify the mistake: A student claims that the gradient of the line through (1,2) and (4,8) is 6.

Answer: Incorrect; gradient = (8-2)/(4-1)=6/3=2

Question 10: A line with positive gradient passes through (0, 0) and (5, 10). What is the gradient? Is it considered steep? Explain.

Answer: Gradient=10/5=2; Yes, it is relatively steep because the slope is greater than 1.

Question 11: Construct a line with a gradient of 0.5 passing through (2, 3). Draw the line on the grid.

Answer: y=0.5(x-2)+3=0.5x+2