Which equation represents a line parallel to 4x - 3y = 6? a. y = x- 3 c. y = x+7 b. y- 7 = -(x + 1) d. 3x – 4y = 12 3.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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ChapterP: Preliminary Concepts
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**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 \
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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