Find the slope of each line in the graph. (HINT: Label your x1,y1,x2,y2 on the line). You must show the slope formula with numbers. 4-2 0 -2 Slope of line a Slope of line b
Find the slope of each line in the graph. (HINT: Label your x1,y1,x2,y2 on the line). You must show the slope formula with numbers. 4-2 0 -2 Slope of line a Slope of line b
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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![### Finding the Slope of a Line
#### Instructions:
Find the slope of each line in the graph. **Hint:** Label your \( x_1, y_1, x_2, y_2 \) on the line. You must show the slope formula with numbers.
#### Explanation of the Graph:
The graph displays two lines, labeled \( a \) and \( b \). The x-axis ranges from -4 to 4, and the y-axis ranges from -4 to 4.
- **Line \( a \):** appears to intersect points (-4, 4) and (0, 0).
- **Line \( b \):** appears to intersect points (-4, -1) and (4, 2).
#### Slope Calculation:
To find the slope of a line, use the formula:
\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]
**Slope of line \( a \):**
1. Choose two points on the line \( a \), for example, \((-4, 4)\) and \((0, 0)\).
2. Substitute into the formula:
\[ m = \frac{0 - 4}{0 - (-4)} = \frac{-4}{4} = -1 \]
**Slope of line \( b \):**
1. Choose two points on the line \( b \), for example, \((-4, -1)\) and \((4, 2)\).
2. Substitute into the formula:
\[ m = \frac{2 - (-1)}{4 - (-4)} = \frac{3}{8} \]
#### Summary:
- **Slope of line \( a \):** \( -1 \)
- **Slope of line \( b \):** \( \frac{3}{8} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30349753-ac03-4e61-ba38-81f239656501%2Faf62716f-226a-4c07-b9a2-e363a1533936%2Fj8zu6mh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Slope of a Line
#### Instructions:
Find the slope of each line in the graph. **Hint:** Label your \( x_1, y_1, x_2, y_2 \) on the line. You must show the slope formula with numbers.
#### Explanation of the Graph:
The graph displays two lines, labeled \( a \) and \( b \). The x-axis ranges from -4 to 4, and the y-axis ranges from -4 to 4.
- **Line \( a \):** appears to intersect points (-4, 4) and (0, 0).
- **Line \( b \):** appears to intersect points (-4, -1) and (4, 2).
#### Slope Calculation:
To find the slope of a line, use the formula:
\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]
**Slope of line \( a \):**
1. Choose two points on the line \( a \), for example, \((-4, 4)\) and \((0, 0)\).
2. Substitute into the formula:
\[ m = \frac{0 - 4}{0 - (-4)} = \frac{-4}{4} = -1 \]
**Slope of line \( b \):**
1. Choose two points on the line \( b \), for example, \((-4, -1)\) and \((4, 2)\).
2. Substitute into the formula:
\[ m = \frac{2 - (-1)}{4 - (-4)} = \frac{3}{8} \]
#### Summary:
- **Slope of line \( a \):** \( -1 \)
- **Slope of line \( b \):** \( \frac{3}{8} \)
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