IDNLearn.com provides a comprehensive solution for all your question and answer needs. Discover detailed answers to your questions with our extensive database of expert knowledge.
Consider the line [tex]y = 2 - 5x[/tex].
1. What is the slope of a line parallel to this line? 2. What is the slope of a line perpendicular to this line?
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].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.
