To determine the slope of a line that is parallel to the given line [tex]\( y = -\frac{1}{5} \)[/tex]:
1. Understand the Slope of the Given Line:
- The equation [tex]\( y = -\frac{1}{5} \)[/tex] is in the slope-intercept form [tex]\( y = mx + b \)[/tex].
- Here, [tex]\( y = -\frac{1}{5} \)[/tex] is a horizontal line because there is no variable [tex]\( x \)[/tex] present in the equation.
- For a horizontal line, the slope [tex]\( m \)[/tex] can be directly read from the equation. In this case, the slope [tex]\( m \)[/tex] is [tex]\( -\frac{1}{5} \)[/tex].
2. Slope of Parallel Lines:
- Lines that are parallel to each other have the same slope. Therefore, any line parallel to the given line [tex]\( y = -\frac{1}{5} \)[/tex] will have the same slope as [tex]\( -\frac{1}{5} \)[/tex].
3. Conclusion:
- The slope of a line that is parallel to the line [tex]\( y = -\frac{1}{5} \)[/tex] is [tex]\( -\frac{1}{5} \)[/tex].
Expressing this in decimal form:
[tex]\[ -\frac{1}{5} = -0.2 \][/tex]
Thus, the slope of the line that is parallel to [tex]\( y = -\frac{1}{5} \)[/tex] is [tex]\(-0.2\)[/tex].
