Answer:
Option (D)
Step-by-step explanation:
We will use the property of perpendicular lines to solve this question.
If the two lines having slopes [tex]m_1[/tex] and [tex]m_2[/tex] are perpendicular,
[tex]m_1\times m_2=-1[/tex]
Given lines are,
Option (A).
y = 4x - 6
[tex]m_1=4[/tex]
y = 4x + 11
[tex]m_2=4[/tex]
[tex]m_1\times m_2=16[/tex]
Lines are not the perpendicular lines.
Option (B).
y = -4x - 6
[tex]m_1=-4[/tex]
y = 4x + 11
[tex]m_2=4[/tex]
[tex]m_1\times m_2=-16[/tex]
Lines are not perpendicular.
Option (C).
y = [tex]\frac{1}{4}x-6[/tex]
[tex]m_1=\frac{1}{4}[/tex]
y = 4x + 11
[tex]m_2=4[/tex]
[tex]m_1\times m_2=1[/tex]
Therefore, lines are not perpendicular.
Option (D).
y = [tex]-\frac{1}{4}x-6[/tex]
[tex]m_1=-\frac{1}{4}[/tex]
y = 4x + 11
[tex]m_2=4[/tex]
[tex]m_1\times m_2=-1[/tex]
Therefore, both the lines are perpendicular.
Option (D) is the answer.
