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

Answer: y = 4x - 5

Question 2: Determine the equation of a line perpendicular to y = -1/2 x + 3 passing through point (4, -1).

Answer: y = 2x - 9

Question 3: Calculate the equation of a line with slope m = -3 passing through (0, 5).

Answer: y = -3x + 5

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

Answer: y = -1/2 x + 5.5

Question 5: Plot the graph of y = -1/3 x + 2 on the grid.

Answer: Student draws line with slope -1/3 and y-intercept 2.

Question 6: A line passes through (1, 2) and is perpendicular to y = 4x - 7. Find its equation.

Answer: y = -1/4 x + 1.75

Question 7: A school wants to design a fence along a line that is perpendicular to the line y = 1/2 x - 4, passing through (6, -2). Write the equation of the fence line.

Answer: y = -2 x + 10

Question 8: If a line has an equation y = -3x + c and is perpendicular to y = 2x + 5, find the value of c if the line passes through (2, 1).

Answer: 7

Question 9: Identify and correct the mistake: Line equation y = 1/2 x - 3 is perpendicular to y = 2x + 1. Is this true? Why or why not?

Answer: No, because slopes are not negative reciprocals; 1/2 and 2 are not negative reciprocals.

Question 10: Find the equation of a line perpendicular to y = -1/4 x + 3 that passes through the point (-2, 5).

Answer: y = 4 x + 3

Question 11: Challenge: Derive the equation of a line perpendicular to y = 3x + 4, passing through the origin, and express your answer in slope-intercept form.

Answer: y = -1/3 x