Question

Please help with question

Answer 1

Explanation:

Property of the perpendicular lines,

If the two lines
`L_1` and
`L_2` having slopes
`m_1` and
`m_2` are perpendicular to each other,

Then
`m_1* m_2=-1`

Equation of line
`L_1` → y = 3x + 5 ------(1)

Equation of line
`L_2` → 6y + 2x = 1 ------- (2)

Slope of line
`L_1`,

`m_1=3`

Slope of line
`L_2`,

6y + 2x = 1

6y = -2x + 1

`y=-(2)/(6)x+(1)/(6)`

`y=-(1)/(3)x+(1)/(6)`

Therefore,
`m_2=-(1)/(3)`

By using the property of perpendicular lines,

`m_1* m_2=3* (-(1)/(3) )`

`=-1`

Therefore, both the lines are perpendicular.