Question 1: Lines that are parallel have the same gradient. The gradient of a line passing through points (x₁, y₁) and (x₂, y₂) is given by (y₂ - y₁) / (x₂ - x₁).

Answer: Same gradient means equal (y₂ - y₁) / (x₂ - x₁) for both lines.

Question 1: Calculate the gradient of the line passing through (2, 5) and (6, 13).

Answer: 2

Question 2: Find the gradient of a line passing through (-3, 4) and (1, 8).

Answer: 2

Question 3: Given a line with gradient 3 passing through (0, 2), write its equation in slope-intercept form.

Answer: y=3x+2

Question 1: Two lines are parallel. Line A passes through (1, 2) and (4, 8). Line B passes through (2, 3) and a point (x, y). Find the coordinates of (x, y) if the gradient of line B is the same as line A.

Answer: x=5, y=9

Question 2: Explain why two lines with different y-intercepts but the same gradient are parallel.

Answer: Because they have the same slope but different intercepts, they never meet and are parallel.

Question 1: A ramp rises 3 meters over a horizontal distance of 4 meters. A second ramp has the same gradient but starts from a different height and distance. If the second ramp starts at height 2 meters, how far horizontally does it extend to maintain the same gradient?

Answer: x=8 meters

Question 1: Construct a line passing through (2, 3) that is parallel to the line y=4x - 1. Then, write its equation.

Answer: y=4x-5

Question 2: Given two lines: y=2x+1 and y=mx+5. Find the value of m if the lines are parallel.

Answer: 2

Question 1: Statement: Two lines with different gradients are parallel. Is this correct? Explain your answer.

Answer: No, lines are parallel only if they have the same gradient.

Question 2: A student claims that lines with the same y-intercept are always parallel. Is this true? Justify your answer.

Answer: No, lines with same y-intercept are the same line; parallel lines require same gradient but different intercepts.