Question

Are the lines -x-5y=7 perpendicular to 5x-y =-9?

Answer 1

Given:

`\begin{gathered} -x-5y=7 \\ 5x-y=-9 \end{gathered}`

Required:

To check whether the lines are perpendicular or not.

Step-by-step explanation:

The slope-intercept form of the lines is,

For the first line,

`\begin{gathered} -x-5y=7 \\ -5y=x+7 \\ y=-(1)/(5)x-(7)/(5) \end{gathered}`

For the second line,

`\begin{gathered} 5x-y=-9 \\ -y=-5x-9 \\ y=5x+9 \end{gathered}`

So, the slope of lines 1 and 2 are,

`\begin{gathered} m_1=-(1)/(5) \\ m_2=5 \end{gathered}`

Since,

`m_1* m_2=(-(1)/(5))(5)=-1`

Therefore, the lines are perpendicular.

Final answer:

The lines are perpendicular.