In order to solve this exercise, you need to remember the following definitions:
1. The slopes of Paralell lines are equal.
2. The slopes of Perpendicular lines are opposite reciprocals.
The equation of a line in Slope-Intercept form is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
In this case you have the following equation of a line written in Slope-Intercept form:
[tex]y=\frac{1}{2}x+6[/tex]So you can identify that the slope of this line is:
[tex]m=\frac{1}{2}[/tex]Therefore, you can determine that the answers are:
-The Slope of a parallel line is:
[tex]m_{\text{par}}=\frac{1}{2}[/tex]- The Slope of a perpendicular line is:
[tex]m_{\text{per}}=-2[/tex]