Answer:
The correct answer is:
Option 2: Yes, because the slopes of lines are negative reciprocals.
Step-by-step explanation:
Given equations of lines are:
Line p: x+2y=1
Line q: y=2x+1
We can determine if two lines are parallel or perpendicular by comparing the slopes of line.
Slope intercept form of line is given by the formula
[tex]y = mx+b[/tex]
Equation of line q is already in slope intercept form.
We have to convert the equation of line p in slope-intercept form
[tex]x+2y = 1\\2y = -x+1\\2y = -\frac{1}{2}x+\frac{1}{2}[/tex]
Slope of line p = 2
Slope of line q = -1/2
We can see that
[tex]2.-\frac{1}{2} = -1[/tex]
The product of slopes of both lines is -1, hence, the lines are perpendicular.
Hence,
The correct answer is:
Option 2: Yes, because the slopes of lines are negative reciprocals.
