The slope of a line that is parallel to 5x – y = 7 is m = The equation of the line (in slope-intercept form) parallel to 5x – Y = 7 that passes through the point ( – 3, – 2) is Y =

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,...
icon
Related questions
Question
### Finding the Slope and Equation of Parallel Lines

**Finding the Slope**

To determine the slope of a line that is parallel to the given line equation:
\[ 5x - y = 7 \]

First, convert the equation into slope-intercept form (\( y = mx + b \)):

\[ 5x - y = 7 \]
\[ -y = -5x + 7 \]
\[ y = 5x - 7 \]

From this, we can see that the slope (\( m \)) of the line is 5.

\[ m = \boxed{5} \]

**Finding the Equation of the Parallel Line**

Next, to find the equation of a line in slope-intercept form that is parallel to \( 5x - y = 7 \) and passes through the point \( (-3, -2) \):

1. We know the slope (\( m \)) is the same: 5.
2. Substitute the slope (\( m = 5 \)) and the given point \( (x_1, y_1) = (-3, -2) \) into the point-slope form of the line equation: 
   \[ y - y_1 = m(x - x_1) \]

\[ y - (-2) = 5(x - (-3)) \]
\[ y + 2 = 5(x + 3) \]
\[ y + 2 = 5x + 15 \]
\[ y = 5x + 13 \]

Hence, the equation of the line parallel to \( 5x - y = 7 \) and passing through \( (-3, -2) \) is:

\[ y = \boxed{5x + 13} \]

By working through these steps, students can learn to find the slope and equation of lines that are parallel to a given line.
Transcribed Image Text:### Finding the Slope and Equation of Parallel Lines **Finding the Slope** To determine the slope of a line that is parallel to the given line equation: \[ 5x - y = 7 \] First, convert the equation into slope-intercept form (\( y = mx + b \)): \[ 5x - y = 7 \] \[ -y = -5x + 7 \] \[ y = 5x - 7 \] From this, we can see that the slope (\( m \)) of the line is 5. \[ m = \boxed{5} \] **Finding the Equation of the Parallel Line** Next, to find the equation of a line in slope-intercept form that is parallel to \( 5x - y = 7 \) and passes through the point \( (-3, -2) \): 1. We know the slope (\( m \)) is the same: 5. 2. Substitute the slope (\( m = 5 \)) and the given point \( (x_1, y_1) = (-3, -2) \) into the point-slope form of the line equation: \[ y - y_1 = m(x - x_1) \] \[ y - (-2) = 5(x - (-3)) \] \[ y + 2 = 5(x + 3) \] \[ y + 2 = 5x + 15 \] \[ y = 5x + 13 \] Hence, the equation of the line parallel to \( 5x - y = 7 \) and passing through \( (-3, -2) \) is: \[ y = \boxed{5x + 13} \] By working through these steps, students can learn to find the slope and equation of lines that are parallel to a given line.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Cartesian Coordinates
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education