Question 1: Find the negative reciprocal of the slope 3/4.

Answer: -4/3

Question 2: Calculate the negative reciprocal of y = -2x + 5.

Answer: 1/2

Question 3: Determine the slope of a line perpendicular to a line with slope 1/3.

Answer: -3

Question 4: If a line has slope -5/8, what is the slope of a line perpendicular to it?

Answer: 8/5

Question 5: Construct a line on the grid with a slope that is the negative reciprocal of y = 7x - 2.

Answer: -1/7

Question 6: Plot the graph of y = -1/2 x + 3 on the grid. Then, draw a line perpendicular to it passing through the origin.

Answer: Student draws the perpendicular line with slope 2 passing through (0,0).

Question 7: A line passes through (2, 3) with slope 4/5. Find the slope of the line perpendicular to it.

Answer: -5/4

Question 8: A student claims that the negative reciprocal of y = -3x + 1 is y = 3x - 1. Is this correct? Explain.

Answer: No, because the negative reciprocal of slope -3 is 1/3, not 3.

Question 9: Identify the mistake in this reasoning: The negative reciprocal of y = 2x is y = -2x.

Answer: The negative reciprocal of 2 is -1/2, not -2.

Question 10: Challenge: Find a pair of perpendicular lines where one has slope 5/7. Write the equations assuming they pass through the origin.

Answer: y = (5/7)x and y = -(7/5)x