instructions in photo **Understanding Parallel Lines in Algebra**When studying algebra, one of the key concepts is understanding how to identify lines that are parallel. Parallel lines never intersect and have the same slope. In this example, we are asked to determine which equation represents a line that is parallel to the given line: \[ y = -2x - 12 \]### Multiple Choice Options:There are four equations to choose from:1. \[ 2y - x = -6 \]2. \[ x + 2y = -10 \]3. \[ 2x - y = 6 \]4. \[ 2x + y = 4 \]### Detailed Analysis:- **Option **: \[ 2y - x = -6 \] - Simplify to slope-intercept form $ y = mx + b $: \[ 2y = x - 6 \] \[ y = \frac{1}{2}x - 3 \] - Slope ($ m $) = $ \frac{1}{2} $- **Option **: \[ x + 2y = -10 \] - Simplify to slope-intercept form $ y = mx + b $: \[ 2y = -x - 10 \] \[ y = -\frac{1}{2}x - 5 \] - Slope ($ m $) = -$ \frac{1}{2} $ - **Option **: \[ 2x - y = 6 \] - Simplify to slope-intercept form $ y = mx + b $: \[ -y = -2x + 6 \] \[ y = 2x - 6 \] - Slope ($ m $) = 2 - **Option **: \[ 2x + y = 4 \] - Simplify to slope-intercept form $ y = mx + b $: \[ y = -2x + 4 \] - Slope ($ m $) = -2 ### Conclusion:To find the line parallel to $ y = -2x - 12 $, we need to identify the equation with a slope of -2. Therefore, the correct equation is:\[ 2x +

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Answered: Which equation represents a line which…

Which equation represents a line which is parallel to the line y = -2x - 1? O x +2y = -10 O 2x-y= 4 %3D O 2y – x = -6 O 2x + y = -6

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

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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instructions in photo

**Understanding Parallel Lines in Algebra**

When studying algebra, one of the key concepts is understanding how to identify lines that are parallel. Parallel lines never intersect and have the same slope. In this example, we are asked to determine which equation represents a line that is parallel to the given line:

\[ y = -2x - 12 \]

### Multiple Choice Options:
There are four equations to choose from:

1. \[ 2y - x = -6 \]
2. \[ x + 2y = -10 \]
3. \[ 2x - y = 6 \]
4. \[ 2x + y = 4 \]

### Detailed Analysis:

- **Option **: \[ 2y - x = -6 \]
- Simplify to slope-intercept form $ y = mx + b $:
\[ 2y = x - 6 \]
\[ y = \frac{1}{2}x - 3 \]
- Slope ($ m $) = $ \frac{1}{2} $

- **Option **: \[ x + 2y = -10 \]
- Simplify to slope-intercept form $ y = mx + b $:
\[ 2y = -x - 10 \]
\[ y = -\frac{1}{2}x - 5 \]
- Slope ($ m $) = -$ \frac{1}{2} $

- **Option **: \[ 2x - y = 6 \]
- Simplify to slope-intercept form $ y = mx + b $:
\[ -y = -2x + 6 \]
\[ y = 2x - 6 \]
- Slope ($ m $) = 2

- **Option **: \[ 2x + y = 4 \]
- Simplify to slope-intercept form $ y = mx + b $:
\[ y = -2x + 4 \]
- Slope ($ m $) = -2

### Conclusion:
To find the line parallel to $ y = -2x - 12 $, we need to identify the equation with a slope of -2. Therefore, the correct equation is:

\[ 2x +

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