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
![**Find the value of \( x \).**
The image features a geometric diagram depicting a parallelogram with labeled sides. The top and bottom sides are parallel and each labeled as \( x \). The left side is indicated as measuring 29 units, and the right side is marked as 23 units. The opposite sides of a parallelogram are congruent.
To solve for \( x \), note the properties of the parallelogram. The opposite sides are equal, implying:
\[ x = 23 \]
Place your solution for \( x \) in the box provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43eb41af-d84b-40c1-ba80-6ea778a40d08%2F05ef2ef8-26a3-4311-87cd-dea9ce8a6321%2F8i8fw5p_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the value of \( x \).**
The image features a geometric diagram depicting a parallelogram with labeled sides. The top and bottom sides are parallel and each labeled as \( x \). The left side is indicated as measuring 29 units, and the right side is marked as 23 units. The opposite sides of a parallelogram are congruent.
To solve for \( x \), note the properties of the parallelogram. The opposite sides are equal, implying:
\[ x = 23 \]
Place your solution for \( x \) in the box provided.
![**Problem Statement:**
Write an equation for the line parallel to the given line that contains point C.
**Given:**
- Point C(2, 8)
- Equation of the line: \( y = -3x + 5 \)
**Solution:**
Since the lines are parallel, they have the same slope. The slope of the given line is \(-3\).
To find the equation of the line parallel to \( y = -3x + 5 \) that passes through the point C(2, 8), use the point-slope form:
\[ y - y_1 = m(x - x_1) \]
Substitute \( m = -3 \), \( x_1 = 2 \), \( y_1 = 8 \):
\[ y - 8 = -3(x - 2) \]
Simplify and rewrite in slope-intercept form (\( y = mx + b \)):
\[ y - 8 = -3x + 6 \]
\[ y = -3x + 14 \]
**Answer:**
The equation of the line is \( y = -3x + 14 \).
(Type your answer in slope-intercept form.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43eb41af-d84b-40c1-ba80-6ea778a40d08%2F05ef2ef8-26a3-4311-87cd-dea9ce8a6321%2Fcjdyylk_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Write an equation for the line parallel to the given line that contains point C.
**Given:**
- Point C(2, 8)
- Equation of the line: \( y = -3x + 5 \)
**Solution:**
Since the lines are parallel, they have the same slope. The slope of the given line is \(-3\).
To find the equation of the line parallel to \( y = -3x + 5 \) that passes through the point C(2, 8), use the point-slope form:
\[ y - y_1 = m(x - x_1) \]
Substitute \( m = -3 \), \( x_1 = 2 \), \( y_1 = 8 \):
\[ y - 8 = -3(x - 2) \]
Simplify and rewrite in slope-intercept form (\( y = mx + b \)):
\[ y - 8 = -3x + 6 \]
\[ y = -3x + 14 \]
**Answer:**
The equation of the line is \( y = -3x + 14 \).
(Type your answer in slope-intercept form.)
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