Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Question:**
Which equation represents a line parallel to \(4x - 3y = 6?\)
**Options:**
a. \( y = \frac{3}{4}x - 3 \)
b. \( y - 7 = -\frac{4}{3}(x + 1) \)
c. \( y = \frac{4}{3}x + 7 \)
d. \( 3x - 4y = 12 \)
Explanation:
To determine which equation represents a line parallel to \( 4x - 3y = 6 \), we need to identify the slope of the given line. A line parallel to \( 4x - 3y = 6 \) will have the same slope.
First, let's rewrite \( 4x - 3y = 6 \) in slope-intercept form \( y = mx + b \):
\[ 4x - 3y = 6 \]
\[ -3y = -4x + 6 \]
\[ y = \frac{4}{3}x - 2 \]
The slope \( m \) of this line is \( \frac{4}{3} \).
Now, compare this slope to the slopes of the lines in the given options:
a. \( y = \frac{3}{4}x - 3 \): The slope is \( \frac{3}{4} \).
b. \( y - 7 = -\frac{4}{3}(x + 1) \):
- Rewrite in slope-intercept form:
\[
y - 7 = -\frac{4}{3}(x + 1) \\
y - 7 = -\frac{4}{3}x - \frac{4}{3} \\
y = -\frac{4}{3}x + \frac{17}{3}
\]
The slope is \( -\frac{4}{3} \).
c. \( y = \frac{4}{3}x + 7 \): The slope is \( \frac{4}{3} \).
d. \( 3x - 4y = 12 \):
- Rewrite in slope-intercept form:
\[
3x - 4y = 12 \\
-4y = -3x + 12 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febcd91cf-c92a-4a76-9c9a-e8d21c0f504d%2F8eabdb28-143b-4ac7-8593-b6936a2ff131%2F1j8een_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Which equation represents a line parallel to \(4x - 3y = 6?\)
**Options:**
a. \( y = \frac{3}{4}x - 3 \)
b. \( y - 7 = -\frac{4}{3}(x + 1) \)
c. \( y = \frac{4}{3}x + 7 \)
d. \( 3x - 4y = 12 \)
Explanation:
To determine which equation represents a line parallel to \( 4x - 3y = 6 \), we need to identify the slope of the given line. A line parallel to \( 4x - 3y = 6 \) will have the same slope.
First, let's rewrite \( 4x - 3y = 6 \) in slope-intercept form \( y = mx + b \):
\[ 4x - 3y = 6 \]
\[ -3y = -4x + 6 \]
\[ y = \frac{4}{3}x - 2 \]
The slope \( m \) of this line is \( \frac{4}{3} \).
Now, compare this slope to the slopes of the lines in the given options:
a. \( y = \frac{3}{4}x - 3 \): The slope is \( \frac{3}{4} \).
b. \( y - 7 = -\frac{4}{3}(x + 1) \):
- Rewrite in slope-intercept form:
\[
y - 7 = -\frac{4}{3}(x + 1) \\
y - 7 = -\frac{4}{3}x - \frac{4}{3} \\
y = -\frac{4}{3}x + \frac{17}{3}
\]
The slope is \( -\frac{4}{3} \).
c. \( y = \frac{4}{3}x + 7 \): The slope is \( \frac{4}{3} \).
d. \( 3x - 4y = 12 \):
- Rewrite in slope-intercept form:
\[
3x - 4y = 12 \\
-4y = -3x + 12 \
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