Answer:
Step-by-step explanation:
Property of the perpendicular lines,
If the two lines [tex]L_1[/tex] and [tex]L_2[/tex] having slopes [tex]m_1[/tex] and [tex]m_2[/tex] are perpendicular to each other,
Then [tex]m_1\times m_2=-1[/tex]
Equation of line [tex]L_1[/tex] → y = 3x + 5 ------(1)
Equation of line [tex]L_2[/tex] → 6y + 2x = 1 ------- (2)
Slope of line [tex]L_1[/tex],
[tex]m_1=3[/tex]
Slope of line [tex]L_2[/tex],
6y + 2x = 1
6y = -2x + 1
[tex]y=-\frac{2}{6}x+\frac{1}{6}[/tex]
[tex]y=-\frac{1}{3}x+\frac{1}{6}[/tex]
Therefore, [tex]m_2=-\frac{1}{3}[/tex]
By using the property of perpendicular lines,
[tex]m_1\times m_2=3\times (-\frac{1}{3} )[/tex]
[tex]=-1[/tex]
Therefore, both the lines are perpendicular.
