Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Are the two lines parallel
![**Question 11a:**
Are the two lines parallel? Show work.
**Graph Explanation:**
The graph displays two lines plotted on a coordinate plane. Each axis is marked from -6 to 6.
**Line Analysis:**
1. **Line 1** passes through the points:
- (-3, 0)
- (3, 2)
2. **Line 2** passes through the points:
- (-1, -3)
- (5, 1)
**Determine Slopes:**
To find if the lines are parallel, the slopes of the lines need to be calculated, as parallel lines have equal slopes.
**Slope Calculation Formula:**
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
**Slope of Line 1:**
\[ m_1 = \frac{2 - 0}{3 - (-3)} = \frac{2}{6} = \frac{1}{3} \]
**Slope of Line 2:**
\[ m_2 = \frac{1 - (-3)}{5 - (-1)} = \frac{4}{6} = \frac{2}{3} \]
**Conclusion:**
Since the slopes \( m_1 \) and \( m_2 \) are not equal (\(\frac{1}{3} \neq \frac{2}{3}\)), the lines are not parallel.](https://content.bartleby.com/qna-images/question/d484bd2f-97bd-4ec9-9ebb-7d25c3dfe832/2764cb70-d834-43e6-be05-32ba662d4df1/kqcnju_processed.jpeg)
Transcribed Image Text:**Question 11a:**
Are the two lines parallel? Show work.
**Graph Explanation:**
The graph displays two lines plotted on a coordinate plane. Each axis is marked from -6 to 6.
**Line Analysis:**
1. **Line 1** passes through the points:
- (-3, 0)
- (3, 2)
2. **Line 2** passes through the points:
- (-1, -3)
- (5, 1)
**Determine Slopes:**
To find if the lines are parallel, the slopes of the lines need to be calculated, as parallel lines have equal slopes.
**Slope Calculation Formula:**
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
**Slope of Line 1:**
\[ m_1 = \frac{2 - 0}{3 - (-3)} = \frac{2}{6} = \frac{1}{3} \]
**Slope of Line 2:**
\[ m_2 = \frac{1 - (-3)}{5 - (-1)} = \frac{4}{6} = \frac{2}{3} \]
**Conclusion:**
Since the slopes \( m_1 \) and \( m_2 \) are not equal (\(\frac{1}{3} \neq \frac{2}{3}\)), the lines are not parallel.
Expert Solution
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Step 1
Given:
Co-ordinates of line l1=(-3,0) and (3,2)
Co-ordinates of line l2=(-1,-3) and (5,-1)
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