Given:
Line A: [tex]y=\frac{1}{2} x+2[/tex]
Line B: [tex]y=\frac{-1}{2} x+7[/tex]
Line C: [tex]y=2 x+4[/tex]
Line D: [tex]y=\frac{1}{2} x+\frac{5}{4}[/tex]
To find:
Which lines are perpendicular
Solution:
General equation of a line:
y = mx + c
where m is the slope and c is the y-intercept.
Slope of line A = [tex]\frac{1}{2}[/tex]
Slope of line B = [tex]\frac{-1}{2}[/tex]
Slope of line C = 2
Slope of line D = [tex]\frac{1}{2}[/tex]
Two lines are perpendicular if their slopes are negative reciprocal of one another.
[tex]$\Rightarrow m_1=\frac{-1}{m_2}[/tex]
[tex]$\frac{-1}{2}=-(-2)=2[/tex]
Negative reciprocal of [tex]\frac{-1}{2}[/tex] is 2.
Therefore line B and line C are perpendicular lines.
