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
![**Mathematics Problem: Finding the Slope Between Two Points on a Graph**
**Problem Statement:**
Find the slope between the two points given below:
\[
(-16, 11), (6, -20)
\]
**Options to choose from:**
A) \(\frac{22}{31}\)
B) \(-\frac{31}{22}\)
C) \(\frac{31}{22}\)
D) \(-\frac{22}{31}\)
**Explanation:**
To find the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) on a graph, use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the given points \((-16, 11)\) and \((6, -20)\):
- \(x_1 = -16\)
- \(y_1 = 11\)
- \(x_2 = 6\)
- \(y_2 = -20\)
Substitute these values into the formula:
\[
m = \frac{-20 - 11}{6 - (-16)} = \frac{-31}{6 + 16} = \frac{-31}{22}
\]
Thus, the slope is:
\[
\boxed{-\frac{31}{22}}
\]
**Correct Answer:**
B) \(-\frac{31}{22}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb294f3d7-c37e-4d19-872e-5bb2e2baac27%2Ffcbd0f49-06f2-490d-bb29-67f8f7afc664%2F8tgz3n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Problem: Finding the Slope Between Two Points on a Graph**
**Problem Statement:**
Find the slope between the two points given below:
\[
(-16, 11), (6, -20)
\]
**Options to choose from:**
A) \(\frac{22}{31}\)
B) \(-\frac{31}{22}\)
C) \(\frac{31}{22}\)
D) \(-\frac{22}{31}\)
**Explanation:**
To find the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) on a graph, use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the given points \((-16, 11)\) and \((6, -20)\):
- \(x_1 = -16\)
- \(y_1 = 11\)
- \(x_2 = 6\)
- \(y_2 = -20\)
Substitute these values into the formula:
\[
m = \frac{-20 - 11}{6 - (-16)} = \frac{-31}{6 + 16} = \frac{-31}{22}
\]
Thus, the slope is:
\[
\boxed{-\frac{31}{22}}
\]
**Correct Answer:**
B) \(-\frac{31}{22}\)
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