Let's consider the line given by the equation [tex]\( y = 2 - 5x \)[/tex].
### Step-by-Step Solution:
#### 1. Identifying the Slope of the Given Line:
The equation of the line is [tex]\( y = 2 - 5x \)[/tex]. This is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- From the equation [tex]\( y = 2 - 5x \)[/tex], we can clearly see that the coefficient of [tex]\( x \)[/tex] is [tex]\( -5 \)[/tex].
- Therefore, the slope [tex]\( m \)[/tex] of the given line is [tex]\( -5 \)[/tex].
#### 2. Slope of a Line Parallel to the Given Line:
- Lines that are parallel to each other have the same slope.
- Hence, the slope of any line parallel to the given line will be the same as the slope of the given line.
Slope of a line parallel to [tex]\( y = 2 - 5x \)[/tex] : [tex]\( -5 \)[/tex]
#### 3. Slope of a Line Perpendicular to the Given Line:
- Lines that are perpendicular to each other have slopes that are negative reciprocals of each other.
- The negative reciprocal of a number [tex]\( m \)[/tex] is [tex]\( -\frac{1}{m} \)[/tex].
- The slope of the given line is [tex]\( -5 \)[/tex].
- Therefore, the negative reciprocal of [tex]\( -5 \)[/tex] is:
[tex]\[
\text{Slope of the perpendicular line} = -\frac{1}{-5} = \frac{1}{5}
\][/tex]
Slope of a line perpendicular to [tex]\( y = 2 - 5x \)[/tex] : [tex]\( \frac{1}{5} \)[/tex]
### Summary:
- The slope of a line parallel to the line [tex]\( y = 2 - 5x \)[/tex] is [tex]\( -5 \)[/tex].
- The slope of a line perpendicular to the line [tex]\( y = 2 - 5x \)[/tex] is [tex]\( \frac{1}{5} \)[/tex].
