9. We have the lines:
[tex]\begin{gathered} y+2=0\rightarrow\text{ a horizontal line with constant value y = -2,} \\ x+2=0\rightarrow\text{ a vertical line with constant value x = -2.} \end{gathered}[/tex]
Plotting the lines, we get the following graph:
From the graph, we see that the lines are perpendicular.
11. We have the lines:
[tex]\begin{gathered} x-5y=4, \\ 5x+y=4. \end{gathered}[/tex]
We rewrite the equations of the lines as:
[tex]\begin{gathered} x-5y=4\rightarrow5y=x-4\rightarrow y=\frac{1}{5}x-\frac{4}{5}, \\ 5x+y=4\rightarrow y=-5x+4. \end{gathered}[/tex]
The general equation of a line with slope m and y-intercept b is:
[tex]y=m\cdot x+b\text{.}[/tex]
The slopes of the lines are:
[tex]\begin{gathered} m_1_{}=\frac{1}{5}, \\ m_2=-5. \end{gathered}[/tex]
Two lines with slopes m1 and m2 are perpendicular if they satisfy the equation:
[tex]m_1\cdot m_2=-1.[/tex]
Replacing the values above, we get:
[tex]m_1\cdot m_2=\frac{1}{5}\cdot(-5)=-1\text{ }✓[/tex]
So we conclude that the lines are perpendicular.
Answer
9. Perpendicular
11. Perpendicular
