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

Answer: y = 3x - 7

Question 2: Determine the equation of a line perpendicular to y = -1/2 x + 4 that passes through the point (6, 2).

Answer: y = 2x - 10

Question 3: Construct the equation of a line with slope -4 that passes through (0, 5).

Answer: y = -4x + 5

Question 4: Identify the slope of the line perpendicular to y = 2x + 3.

Answer: -1/2

Question 5: Find the equation of a line parallel to y = -3x + 2 that passes through (4, -2).

Answer: y = -3x + 10

Question 6: A line passes through (1, 2) and has an equation y = 4x + c. Find c and write the full equation.

Answer: c = -2; y = 4x - 2

Question 7: Plot the graph of y = -1/3 x + 2 and y = 3x - 4 on the grid provided.

Answer: Students plot the two lines.

Question 8: Construct a triangle with vertices at (0,0), (2,4), and (4,0). Find the equations of the lines perpendicular to the base (between points (0,0) and (4,0)) passing through the opposite vertices.

Answer: Lines: y = 0.5x and y = -0.5x + 4

Question 9: A line has the equation y = 2x + 1. What is the equation of the line perpendicular to it passing through (3, 4)?

Answer: y = -1/2 x + 5

Question 10: Identify and correct the mistake: The line y = 5x - 2 is perpendicular to y = 1/5 x + 3.

Answer: Correct slope for perpendicular line is -1/5; the given line is parallel, not perpendicular.

Question 11: Challenge: Find the equation of a line perpendicular to y = -2x + 3 that passes through the point (-1, 4).

Answer: y = 1/2 x + 3.5