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.

Explanation:

The slope-intercept form of the lines is,

For the first line,

$\begin{gathered} -x-5y=7 \\ -5y=x+7 \\ y=-\frac{1}{5}x-\frac{7}{5} \end{gathered}$

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,

$\begin{gathered} m_1=-\frac{1}{5} \\ m_2=5 \end{gathered}$

Since,

$m_1\times m_2=(-\frac{1}{5})(5)=-1$

Therefore, the lines are perpendicular.

Final answer:

The lines are perpendicular.