Question 1: What is the negative reciprocal of the slope 3/4?

Answer: -4/3

Question 2: Calculate the slope of a line perpendicular to a line with slope -2/5.

Answer: 5/2

Question 3: Construct a line on the grid that is perpendicular to the line y=2x+1. You may draw the line.

Answer: line with slope -1/2 passing through a chosen point

Question 4: Identify the mistake in this statement: “The negative reciprocal of 7/3 is 7/3”.

Answer: The mistake is that the negative reciprocal should be -3/7, not 7/3.

Question 5: Find the equation of a line perpendicular to 3x - 4y = 7 that passes through the point (2, -1).

Answer: y + 1 = (3/4)(x - 2)

Question 6: A line has a slope of 5. What is the slope of a line perpendicular to it? Show your working.

Answer: -1/5

Question 7: Plot the graph of y = -1/2 x + 3 and draw a line perpendicular to it passing through (0, 3).

Answer: Line with slope 2 passing through (0, 3)

Question 8: A line with slope 4 is perpendicular to a line with slope m. Write an algebraic expression for m and explain your reasoning.

Answer: m = -1/4 because the negative reciprocal of 4 is -1/4.

Question 9: Extend the line y = -3x + 2 to a new line perpendicular to it passing through (1, 0). Write the equation.

Answer: y + 0 = (1/3)(x - 1)

Question 10: Identify the common mistake in calculating the negative reciprocal of -8/5 and correct it.

Answer: Common mistake: Using the same fraction without changing the sign. Correct reciprocal: 5/8.

Question 11: A school wants to design a playground layout with paths perpendicular to each other. If one path has slope 2, what should be the slope of the perpendicular path?

Answer: -1/2