Question 103 of 190 FINAL - Mathematics Which statement best describes the relationship between lines M and N? M (2,7) (1,4)- 3) A. Line M has a positive slope, and line N has a negative slope. B. Line M has a negative slope, and line N has a positive slope. C. Line M and line N both have positive slopes. D. Line M and line N both have negative slopes. E. There is not enough information to calculate the slopes of line N and line M. (3,5)
Question 103 of 190 FINAL - Mathematics Which statement best describes the relationship between lines M and N? M (2,7) (1,4)- 3) A. Line M has a positive slope, and line N has a negative slope. B. Line M has a negative slope, and line N has a positive slope. C. Line M and line N both have positive slopes. D. Line M and line N both have negative slopes. E. There is not enough information to calculate the slopes of line N and line M. (3,5)
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
100%
![### Question 103 of 190
**FINAL - Mathematics**
**Which statement best describes the relationship between lines M and N?**
#### Diagram Analysis:
The diagram presents a Cartesian coordinate system with two lines, labeled M and N, intersecting at different points.
Here are the coordinates for the lines shown in the graph:
- **Line M**:
- Passes through the points (1, 3) and (4, 5)
- **Line N**:
- Passes through the points (1, 4) and (2, 7)
#### Calculation of Slopes:
To determine the relationship between the slopes of the lines, we will calculate the slope (m) of each line using the formula:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
**Line M**:
- Points: (1, 3) and (4, 5)
- Slope (m) of Line M:
\[ m = \frac{5 - 3}{4 - 1} = \frac{2}{3} \]
**Line N**:
- Points: (1, 4) and (2, 7)
- Slope (m) of Line N:
\[ m = \frac{7 - 4}{2 - 1} = \frac{3}{1} = 3 \]
#### Answer Choices Evaluation:
- **A.** Line M has a positive slope, and line N has a negative slope.
- **B.** Line M has a negative slope, and line N has a positive slope.
- **C.** Line M and line N both have positive slopes.
- **D.** Line M and line N both have negative slopes.
- **E.** There is not enough information to calculate the slopes of line N and line M.
Based on the calculated slopes:
- Line M has a slope of \( \frac{2}{3} \), which is positive.
- Line N has a slope of \( 3 \), which is also positive.
Thus, the correct answer is:
**C. Line M and line N both have positive slopes.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc22a9166-79ef-4489-a230-81be74daa87f%2F4a2f36be-db13-498e-8ca8-a8b2aa770ceb%2Fy6vowgh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 103 of 190
**FINAL - Mathematics**
**Which statement best describes the relationship between lines M and N?**
#### Diagram Analysis:
The diagram presents a Cartesian coordinate system with two lines, labeled M and N, intersecting at different points.
Here are the coordinates for the lines shown in the graph:
- **Line M**:
- Passes through the points (1, 3) and (4, 5)
- **Line N**:
- Passes through the points (1, 4) and (2, 7)
#### Calculation of Slopes:
To determine the relationship between the slopes of the lines, we will calculate the slope (m) of each line using the formula:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
**Line M**:
- Points: (1, 3) and (4, 5)
- Slope (m) of Line M:
\[ m = \frac{5 - 3}{4 - 1} = \frac{2}{3} \]
**Line N**:
- Points: (1, 4) and (2, 7)
- Slope (m) of Line N:
\[ m = \frac{7 - 4}{2 - 1} = \frac{3}{1} = 3 \]
#### Answer Choices Evaluation:
- **A.** Line M has a positive slope, and line N has a negative slope.
- **B.** Line M has a negative slope, and line N has a positive slope.
- **C.** Line M and line N both have positive slopes.
- **D.** Line M and line N both have negative slopes.
- **E.** There is not enough information to calculate the slopes of line N and line M.
Based on the calculated slopes:
- Line M has a slope of \( \frac{2}{3} \), which is positive.
- Line N has a slope of \( 3 \), which is also positive.
Thus, the correct answer is:
**C. Line M and line N both have positive slopes.**
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning