To find the slope of a line perpendicular to the given line, we will follow these steps:
1. Determine the slope of the given line:
- Start with the given equation of the line: [tex]\( 5x - y = -7 \)[/tex].
- To easily identify the slope, we need to rearrange this into the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope.
- Let's rearrange the given equation:
[tex]\[
5x - y = -7
\][/tex]
Isolate [tex]\( y \)[/tex] on one side:
[tex]\[
-y = -5x - 7
\][/tex]
Multiply through by [tex]\(-1\)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 5x + 7
\][/tex]
In this form, it is now clear that the slope [tex]\( m \)[/tex] of the given line is 5.
2. Find the slope of the perpendicular line:
- Remember, for two lines to be perpendicular, the product of their slopes must be [tex]\(-1\)[/tex]. This means if one line has a slope [tex]\( m \)[/tex], the perpendicular line will have a slope of [tex]\(-\frac{1}{m}\)[/tex].
- Given the slope [tex]\( m \)[/tex] of the original line is 5, the slope of the perpendicular line will therefore be:
[tex]\[
-\frac{1}{5} = -0.2
\][/tex]
So, the slope of a line perpendicular to the line [tex]\( 5x - y = -7 \)[/tex] is [tex]\( -0.2 \)[/tex].
