Which statement is true about a line that runs parallel to the x-axis and passes through the point (-4, 13)? (1) It has a slope of zero and a equation of x -4. (2) It has an undefined slope and an equation ofx=-4. (3) It has a slope of zero and an equation of y 13. (4) It has an undefined slope and an equation of y 13.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**Understanding Lines Parallel to the X-Axis**

### Question:
Which statement is true about a line that runs parallel to the x-axis and passes through the point \((-4, 13)\)?

### Options:
1. It has a slope of zero and an equation of \( x = -4 \).
2. It has an undefined slope and an equation of \( x = -4 \).
3. It has a slope of zero and an equation of \( y = 13 \).
4. It has an undefined slope and an equation of \( y = 13 \).

### Analysis:
1. **Slope of zero**: A line parallel to the x-axis is horizontal, which means its slope is zero.
2. **Equation of the line**: For a horizontal line passing through the point \((-4, 13)\), the equation of the line is based on the y-coordinate. Therefore, the equation would be \(y = 13\).

### Correct Answer:
3. It has a slope of zero and an equation of \( y = 13 \).
Transcribed Image Text:**Understanding Lines Parallel to the X-Axis** ### Question: Which statement is true about a line that runs parallel to the x-axis and passes through the point \((-4, 13)\)? ### Options: 1. It has a slope of zero and an equation of \( x = -4 \). 2. It has an undefined slope and an equation of \( x = -4 \). 3. It has a slope of zero and an equation of \( y = 13 \). 4. It has an undefined slope and an equation of \( y = 13 \). ### Analysis: 1. **Slope of zero**: A line parallel to the x-axis is horizontal, which means its slope is zero. 2. **Equation of the line**: For a horizontal line passing through the point \((-4, 13)\), the equation of the line is based on the y-coordinate. Therefore, the equation would be \(y = 13\). ### Correct Answer: 3. It has a slope of zero and an equation of \( y = 13 \).
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