Question 1: Find the equation of the line passing through the point (2, 3) with a slope of 4.

Answer: y=4x-5

Question 2: Calculate the equation of a line parallel to y = -2x + 1 and passing through (4, -3).

Answer: y=-2x+5

Question 3: Construct the equation of a line perpendicular to y = 3x - 4 that passes through (1, 2).

Answer: y=-rac{1}{3}x+rac{7}{3}

Question 4: Write the equation of the line that has a slope of 2 and passes through the point (0, -4).

Answer: y=2x-4

Question 5: Find the equation of a line parallel to y = rac{1}{2}x + 3 and passing through (6, 5).

Answer: y=rac{1}{2}x-rac{1}{2}

Question 6: A line passes through (3, 4) and has an equation y=2x+1. Find the equation of a line parallel to it passing through (5, 8).

Answer: y=2x+1

Question 7: A line has the equation y=-rac{1}{3}x+2. Find the equation of a line parallel to it passing through (0, 4).

Answer: y=-rac{1}{3}x+4

Question 8: A line with equation y=5x-7 passes through point (2, 3). Write the equation of a line parallel to it passing through (2, 1).

Answer: y=5x-7

Question 9: Find the equation of the line passing through (1, -2) with a slope of -rac{3}{4}.

Answer: y=-rac{3}{4}x-rac{5}{4}

Question 10: A line passes through (0, 0) and (4, 8). Find its equation and then write the equation of a parallel line passing through (2, 5).

Answer: First line: y=2x; Parallel line: y=2x+1

Question 11: A student wrote the equation y=3x+2 for a line parallel to y=3x-4. The student made a mistake. Explain the error and provide the correct equation.

Answer: Incorrect: y=3x+2 changes the y-intercept, but the slope should be the same as y=3x-4, which is 3. The correct equations are y=3x+6 or y=3x-4 (parallel lines with same slope).