Question
The equations of three lines are giwen belous.
Line
Line
Line 3:4x+16y=-16
For each pair of lines, determine whether they are paraliel, perpendicular, or meithet
Line 1 and Line 2 - Parallel Perpendicular Neither
Line 1 and Line 3: Parallel Perpendicular Nether
Line 2 and Line 3 : Paraliel Perpendicular Neither
Line
Line 3:4x+16y=-16
For each pair of lines, determine whether they are paraliel, perpendicular, or meithet
Ask by Gordon Luna. in the United States
Mar 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
- Line 1 and Line 2: Neither
- Line 1 and Line 3: Perpendicular
- Line 2 and Line 3: Neither
Solution
To determine the relationship between the lines, we need to find the slopes of each line.
- Line 1: The equation is given as
. The slope is -4. - Line 2: The equation is given as
. We can rewrite it in slope-intercept form by isolating : The slope is . - Line 3: The equation is
. We can rewrite it in slope-intercept form: The slope is .
Now we will compare the slopes to determine if the lines are parallel, perpendicular, or neither.
-
Line 1 and Line 2:
-
-
- Lines are parallel if
, perpendicular if , and neither otherwise.
-
-
Line 1 and Line 3:
-
-
- Check for parallelism and perpendicularity.
-
-
Line 2 and Line 3:
-
-
- Check for parallelism and perpendicularity.
-
Now we will analyze each pair:
-
Line 1 and Line 2:
- For parallel:
implies . - For perpendicular:
implies . - Conclusion: Neither (unless
).
- For parallel:
-
Line 1 and Line 3:
- Check for perpendicular:
. - Conclusion: Perpendicular.
- Check for perpendicular:
-
Line 2 and Line 3:
- For parallel:
implies . - For perpendicular:
implies . - Conclusion: Neither (unless specific values of
).
- For parallel:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Beyond the Answer
To determine the relationships between the lines, we first need to analyze their slopes.
For Line 1, written as
For Line 2, rewriting the equation
For Line 3, converting
Now, we evaluate the pairs of lines:
- Line 1 and Line 2: Without clarification on
, we can’t definitively say if they are parallel, perpendicular, or neither. - Line 1 and Line 3: With
and , since , they are perpendicular. - Line 2 and Line 3: Similar to the first line pair, without knowing
, we can’t categorize this relationship.
To directly answer based on the assumptions:
- Line 1 and Line 2: Neither (depending on
). - Line 1 and Line 3: Perpendicular.
- Line 2 and Line 3: Neither (again, depending on
).
Hope this helps clear up the relationships! Just make sure to check the values behind variables for a smoother ride!
