Find an equation of the line parallel to 7x-y=5 and passing through (4,3). Express the equation in standard form. Which of the following is the equation of a line parallel to 7x - y = 5 and passing through (4,3)? 4 OA. 7x-y=25 OB. 7x-y-31 OC. x+7y=25 O D. x + 7y=31
Find an equation of the line parallel to 7x-y=5 and passing through (4,3). Express the equation in standard form. Which of the following is the equation of a line parallel to 7x - y = 5 and passing through (4,3)? 4 OA. 7x-y=25 OB. 7x-y-31 OC. x+7y=25 O D. x + 7y=31
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![### Question 4 of 20
**Problem Statement:**
Find an equation of the line parallel to \(7x - y = 5\) and passing through \((4, 3)\). Express the equation in standard form.
**Question:**
Which of the following is the equation of a line parallel to \(7x - y = 5\) and passing through \((4, 3)\)?
**Options:**
- A. \(7x - y = 25\)
- B. \(7x - y = 31\)
- C. \(x + 7y = 25\)
- D. \(x + 7y = 31\)
**Explanation:**
Parallel lines have the same slope. The given line’s equation is \(7x - y = 5\).
Rewrite the given line’s equation in slope-intercept form (y = mx + b):
\[ y = 7x - 5 \]
The slope \( m \) is 7.
For the line to be parallel, it must have the same slope \( m = 7 \).
Use the point \((4, 3)\) to find the new line’s equation:
Substitute \( (x, y) = (4, 3) \) and \( m = 7 \) into the point-slope form:
\[ y - 3 = 7(x - 4) \]
\[ y - 3 = 7x - 28 \]
\[ y = 7x - 25 \]
Rewrite in standard form by rearranging:
\[ 7x - y = 25 \]
So, the answer is option A: \(7x - y = 25\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd09747b2-6fd0-4c98-9885-dba015896f0f%2F3d073c8f-56c5-4e05-ac6b-ee451d23816e%2Fcq1ljud_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 4 of 20
**Problem Statement:**
Find an equation of the line parallel to \(7x - y = 5\) and passing through \((4, 3)\). Express the equation in standard form.
**Question:**
Which of the following is the equation of a line parallel to \(7x - y = 5\) and passing through \((4, 3)\)?
**Options:**
- A. \(7x - y = 25\)
- B. \(7x - y = 31\)
- C. \(x + 7y = 25\)
- D. \(x + 7y = 31\)
**Explanation:**
Parallel lines have the same slope. The given line’s equation is \(7x - y = 5\).
Rewrite the given line’s equation in slope-intercept form (y = mx + b):
\[ y = 7x - 5 \]
The slope \( m \) is 7.
For the line to be parallel, it must have the same slope \( m = 7 \).
Use the point \((4, 3)\) to find the new line’s equation:
Substitute \( (x, y) = (4, 3) \) and \( m = 7 \) into the point-slope form:
\[ y - 3 = 7(x - 4) \]
\[ y - 3 = 7x - 28 \]
\[ y = 7x - 25 \]
Rewrite in standard form by rearranging:
\[ 7x - y = 25 \]
So, the answer is option A: \(7x - y = 25\).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education