What is the slope of this line? -8 -7 -6 -5 -4 -3 (-3, -2) -2 8 7 6 LO -4 3 2 -1 234 LO -2 -3 -4 -5 -6- -7- -8. 1 2 LO 3 4 5 6 (6,4) 7 8 X Simplify your answer and write it as a proper fraction, improper fraction, or integer.
What is the slope of this line? -8 -7 -6 -5 -4 -3 (-3, -2) -2 8 7 6 LO -4 3 2 -1 234 LO -2 -3 -4 -5 -6- -7- -8. 1 2 LO 3 4 5 6 (6,4) 7 8 X Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Title: Understanding the Slope of a Line**
**Question: What is the slope of this line?**
The image displays a Cartesian coordinate grid with an x-axis ranging from -8 to 8 and a y-axis ranging from -8 to 8. A green line intersects the grid, passing through the two points (-3, -2) and (6, 4).
**Points on the Line:**
- The first point is labeled as (-3, -2).
- The second point is labeled as (6, 4).
**Instructions:**
- Simplify your answer and write it as a proper fraction, improper fraction, or integer.
**Graph Explanation:**
To determine the slope of the line, use the formula for slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the coordinates of the two points:
\[
m = \frac{4 - (-2)}{6 - (-3)} = \frac{4 + 2}{6 + 3} = \frac{6}{9}
\]
Simplify the fraction:
\[
m = \frac{2}{3}
\]
**Input Box:**
- There is a box to enter your answer, followed by a green "Submit" button.
**Additional Help:**
- A note at the bottom reads: "Work it out. Not feeling ready yet? These can help."
This exercise provides practice in finding the slope of a line by accurately using the formula and simplifying the result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fae2b2b-cf34-4e31-842d-710010ff95bb%2F0ab54692-255c-440c-91ae-b5f65aac6d29%2Fudq2kz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding the Slope of a Line**
**Question: What is the slope of this line?**
The image displays a Cartesian coordinate grid with an x-axis ranging from -8 to 8 and a y-axis ranging from -8 to 8. A green line intersects the grid, passing through the two points (-3, -2) and (6, 4).
**Points on the Line:**
- The first point is labeled as (-3, -2).
- The second point is labeled as (6, 4).
**Instructions:**
- Simplify your answer and write it as a proper fraction, improper fraction, or integer.
**Graph Explanation:**
To determine the slope of the line, use the formula for slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the coordinates of the two points:
\[
m = \frac{4 - (-2)}{6 - (-3)} = \frac{4 + 2}{6 + 3} = \frac{6}{9}
\]
Simplify the fraction:
\[
m = \frac{2}{3}
\]
**Input Box:**
- There is a box to enter your answer, followed by a green "Submit" button.
**Additional Help:**
- A note at the bottom reads: "Work it out. Not feeling ready yet? These can help."
This exercise provides practice in finding the slope of a line by accurately using the formula and simplifying the result.
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