Question

Which of the following lines are perpendicular to the line y = -1/2x + 4? You may choose more than one answer.

a) 2x - y = 1
b) y = 2x
c) 2x + y = 1
d) 1/2x - y = 3
e) 2x - y = 3

Answer 1

Lines a) and b) are perpendicular to y = -1/2x + 4.

Step-by-step explanation:

To determine which of the given lines are perpendicular to the line y = -1/2x + 4, we need to find the negative reciprocal of the slope of the given line. The slope of y = -1/2x + 4 is -1/2. The negative reciprocal of -1/2 is 2.

Now, let's check the slopes of the given lines:

a) 2x - y = 1: The slope is 2, which is the negative reciprocal of -1/2.

b) y = 2x: The slope is 2, which is the negative reciprocal of -1/2.

c) 2x + y = 1: The slope is -2, which is not the negative reciprocal of -1/2.

d) 1/2x - y = 3: The slope is 1/2, which is not the negative reciprocal of -1/2.

e) 2x - y = 3: The slope is 2, which is the negative reciprocal of -1/2.

Therefore, the lines a) and b) are perpendicular to y = -1/2x + 4.