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 =
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,...
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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5857e75-5376-4393-9985-ff706b1962bd%2Fdedeb6dd-65d2-4bb6-a5c3-2736a21a456c%2Fdhf8j9j_processed.jpeg&w=3840&q=75)
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.
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