To understand the slopes of lines parallel and perpendicular to the given line [tex]\( y = 8x - 2 \)[/tex], let’s start by examining this line.
1. Identifying the slope of the given line:
- The line is given 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.
- For the line [tex]\( y = 8x - 2 \)[/tex], the coefficient of [tex]\( x \)[/tex] is 8, which means the slope of this line is 8.
2. Slope of a line parallel to the given line:
- Lines that are parallel to each other have the same slope.
- Therefore, the slope of any line parallel to [tex]\( y = 8x - 2 \)[/tex] will also be 8.
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].
- For our given line with slope 8, the negative reciprocal is [tex]\( -\frac{1}{8} \)[/tex].
So, the solution can be summarized as follows:
- Slope of a parallel line: 8
- Slope of a perpendicular line: [tex]\( -\frac{1}{8} \)[/tex] or approximately [tex]\(-0.125\)[/tex]
Typed out:
- Slope of a parallel line: 8
- Slope of a perpendicular line: [tex]\(-0.125\)[/tex]
