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

Answer: y=2x+(-2)

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

Answer: y=2x-3

Question 3: Calculate the slope of the line perpendicular to the line 3x - 4y = 7.

Answer: m=3/4

Question 4: Construct the equation of a line perpendicular to y = 5x + 1 that passes through the origin. Write your answer in slope-intercept form.

Answer: y=-rac{1}{5}x

Question 5: Determine the equation of a line passing through (-2, 3) and perpendicular to the line y = x - 4.

Answer: y=-2x-1

Question 6: Given the line y=3x+2, find the equation of a line perpendicular to it that passes through the point (0, 0).

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

Question 7: A line has the equation y=4x+1. What is the equation of the line perpendicular to it that passes through the point (2, 0)?

Answer: y=-rac{1}{4}x+ rac{1}{2}

Question 8: A line passing through (1, 2) has an unknown slope m. It is perpendicular to the line y= x - 3. Find the value of m and write the equation of the line.

Answer: m=-rac{1}{6}, y=-rac{1}{6}x+ rac{13}{6}

Question 9: Determine the slope of a line perpendicular to 2x - y = 8.

Answer: m=2

Question 10: Identify and correct the mistake in this student answer: The line y = x + 3 is perpendicular to y = -x + 1. The perpendicular line is y = x - 3.

Answer: Corrected answer: y= rac{1}{2}x + c (with proper perpendicular slope of 2)