Concept explainers
To identify each pair of parallel and perpendicular lines.
Answer to Problem 27PPE
Line ‘a’ and Line ‘f’ are parallel to each other.
Line ‘b’ and Line ‘d’ are perpendicular to each other.
Line ‘c’ and Line ‘e’ are perpendicular to each other.
Explanation of Solution
Given :
Line ‘a’ :
Line ‘d’ :
Formula :
Two lines are parallel to each other if their slopes are equal.
Two lines are perpendicular to each other if the product of their slopes is -1.
Calculation :
First let us calculate slopes of the given equations.
1.Slope of line ‘a’ =
Line ‘b’ is a vertical line perpendicular to the x-axis.
2. Hence, slope of line ‘b’ = 0
3. Slope of line ‘c’ =
Line ‘d’ is a horizontal line parallel to the x-axis.
4. Hence, slope of line ‘b’ = Undefined
5. Slope of line ‘e’ =
Line ‘f’ can be rewritten as
6.Hence, slope of line ‘f’ =
Conclusion :
Clearly, Line ‘b’ and Line ‘d’ are “perpendicular” to each other as one line is vertical to x-axis and the other one is horizontal to the x-axis.
Also, Line ‘a’ and Line ‘f’ are “parallel” to each other as their slopes are equal.
Finally, Line ‘c’ and Line ‘e’ are “perpendicular” to each other since the product of their slopes is -1.
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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