Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
Write the equation of the line that passes through the point \( P(0, 0) \) and is parallel to the line \( y = 8x - 7 \).
**Options:**
1. \( x = 8y \)
2. \( y = 7x + 8 \)
3. \( y = -7x \) (selected option)
4. \( y = 8x \)
5. \( y = 7x \)
**Solution Explanation:**
To solve this problem, the equation of the line must be parallel to \( y = 8x - 7 \). Parallel lines share the same slope. Therefore, the new line must have a slope of 8.
Given that the line passes through the point \( P(0, 0) \), which is the y-intercept. The equation of the line can be written as:
\[ y = 8x + b \]
Since the line goes through the origin \( (0, 0) \), we substitute these values into the equation:
\[ 0 = 8 \cdot 0 + b \]
This results in \( b = 0 \). Therefore, the equation of the line is:
\[ y = 8x \]
Thus, the correct option should be:
4. \( y = 8x \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c568328-9c88-4125-9322-2592809e36a0%2Ff42105c8-fa8b-4683-a308-c1637f7475c5%2Fiy648c_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Write the equation of the line that passes through the point \( P(0, 0) \) and is parallel to the line \( y = 8x - 7 \).
**Options:**
1. \( x = 8y \)
2. \( y = 7x + 8 \)
3. \( y = -7x \) (selected option)
4. \( y = 8x \)
5. \( y = 7x \)
**Solution Explanation:**
To solve this problem, the equation of the line must be parallel to \( y = 8x - 7 \). Parallel lines share the same slope. Therefore, the new line must have a slope of 8.
Given that the line passes through the point \( P(0, 0) \), which is the y-intercept. The equation of the line can be written as:
\[ y = 8x + b \]
Since the line goes through the origin \( (0, 0) \), we substitute these values into the equation:
\[ 0 = 8 \cdot 0 + b \]
This results in \( b = 0 \). Therefore, the equation of the line is:
\[ y = 8x \]
Thus, the correct option should be:
4. \( y = 8x \)
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