Complete the table. y + 1 = -X -2 0 1 Alu y 00000 (x, y)
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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![**Complete the Table**
Consider the equation: \( y + 1 = \frac{4}{5}x \)
You need to complete the table given this equation. For each \(x\) value, solve for the corresponding \( y \) and the \((x, y)\) pair.
Below is the table with columns for \( x \), \( y \), and the ordered pair \((x, y)\):
| \(x\) | \( y \) | \(( x, y )\) |
|------|-------|-------------|
| -2 | | (\_\_, \_\_) |
| 0 | | (\_\_, \_\_) |
| 1 | | (\_\_, \_\_) |
| 5/4 | | (\_\_, \_\_) |
| 2 | | (\_\_, \_\_) |
*Notes on Solving the Table:*
1. For each row, substitute the given \( x \) value into the equation \( y + 1 = \frac{4}{5}x \).
2. Solve for \( y \).
3. Record the \((x, y)\) pair in the respective row.
Let's solve for one row as an example:
For \( x = -2 \):
\[ y + 1 = \frac{4}{5}(-2) \]
\[ y + 1 = -\frac{8}{5} \]
\[ y = -\frac{8}{5} - 1 \]
\[ y = -\frac{8}{5} - \frac{5}{5} \]
\[ y = -\frac{13}{5} \]
So, for \( x = -2 \):
\(( x, y ) = (-2, -\frac{13}{5}) \)
Complete the remaining values using this method and fill in the table accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb5ff0f4-c9f6-49ea-9161-fbb64a60fa05%2F9cef617e-1b51-4ef5-9284-63c399a22292%2F1a0unbe_processed.png&w=3840&q=75)
Transcribed Image Text:**Complete the Table**
Consider the equation: \( y + 1 = \frac{4}{5}x \)
You need to complete the table given this equation. For each \(x\) value, solve for the corresponding \( y \) and the \((x, y)\) pair.
Below is the table with columns for \( x \), \( y \), and the ordered pair \((x, y)\):
| \(x\) | \( y \) | \(( x, y )\) |
|------|-------|-------------|
| -2 | | (\_\_, \_\_) |
| 0 | | (\_\_, \_\_) |
| 1 | | (\_\_, \_\_) |
| 5/4 | | (\_\_, \_\_) |
| 2 | | (\_\_, \_\_) |
*Notes on Solving the Table:*
1. For each row, substitute the given \( x \) value into the equation \( y + 1 = \frac{4}{5}x \).
2. Solve for \( y \).
3. Record the \((x, y)\) pair in the respective row.
Let's solve for one row as an example:
For \( x = -2 \):
\[ y + 1 = \frac{4}{5}(-2) \]
\[ y + 1 = -\frac{8}{5} \]
\[ y = -\frac{8}{5} - 1 \]
\[ y = -\frac{8}{5} - \frac{5}{5} \]
\[ y = -\frac{13}{5} \]
So, for \( x = -2 \):
\(( x, y ) = (-2, -\frac{13}{5}) \)
Complete the remaining values using this method and fill in the table accordingly.
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