Final answer:
Option B is correct. Without the given line's equation, we analyze the slopes of the provided lines: 2 for line (a), 1 for line (b), and -1 for line (c). None are perpendicular unless the original line's slope is -1, making line (b) perpendicular to it.
Step-by-step explanation:
The subject of this question is determining which given lines are perpendicular to a certain line. To ascertain this, one must first understand that perpendicular lines have slopes that are negative reciprocals of each other.
If the slope of the given line is 'm,' then the slope of a line perpendicular to it will be '-1/m.'
We are not provided with the equation for the line we are comparing against, but we can analyze the slopes of the provided lines. Line (a) y = 2x - 4 has a slope of 2.
Line (b) y = x + 3 has a slope of 1. Line (c) y = -x can be assumed as the third option despite the typo; it has a slope of -1.
If we consider a line with a slope of 'm' where m is not displayed in the question, then the line that would be perpendicular to this hypothetical line would have a slope of '-1/m.'
By comparing this to the slopes of the provided lines, none of them would be perpendicular unless the original line's slope was -1, in which case line (b) would be perpendicular because its slope is the negative reciprocal of -1.
Option B is correct
The complete question is:Which of the following lines are perpendicular to the given line.
a. y= 2x - 4
b. y=x+3
c. +3
c. y=-x+