Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Problem Statement:**
Find the equation of the line in slope-intercept form perpendicular to the line given by the equation \(6x - 6y = -3\) and passing through the point \((12, 2)\).
**Solution:**
To find the equation of the line in slope-intercept form, follow these steps:
1. **Rewrite the given equation** \(6x - 6y = -3\) in slope-intercept form \(y = mx + b\).
2. **Determine the slope** of the given line. Simplifying the equation, you get:
\[
6x - 6y = -3 \implies -6y = -6x - 3 \implies y = x + \frac{1}{2}
\]
Therefore, the slope of the given line is \(m = 1\).
3. **Find the slope of the perpendicular line**. The slope of the line perpendicular to one with slope \(m\) is \(-\frac{1}{m}\). Thus, the perpendicular slope is \(-1\).
4. **Use the point-slope form** of the equation with the point \((12, 2)\) and perpendicular slope \(-1\):
\[
y - 2 = -1(x - 12)
\]
5. **Convert to slope-intercept form**:
\[
y - 2 = -x + 12 \implies y = -x + 14
\]
Thus, the equation of the line in slope-intercept form is \(y = -x + 14\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99db74cb-a52b-4540-9e19-530fc4ba7537%2Ffdb39a91-90e2-40e7-ba14-2586d73f2431%2Fd64galb_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the equation of the line in slope-intercept form perpendicular to the line given by the equation \(6x - 6y = -3\) and passing through the point \((12, 2)\).
**Solution:**
To find the equation of the line in slope-intercept form, follow these steps:
1. **Rewrite the given equation** \(6x - 6y = -3\) in slope-intercept form \(y = mx + b\).
2. **Determine the slope** of the given line. Simplifying the equation, you get:
\[
6x - 6y = -3 \implies -6y = -6x - 3 \implies y = x + \frac{1}{2}
\]
Therefore, the slope of the given line is \(m = 1\).
3. **Find the slope of the perpendicular line**. The slope of the line perpendicular to one with slope \(m\) is \(-\frac{1}{m}\). Thus, the perpendicular slope is \(-1\).
4. **Use the point-slope form** of the equation with the point \((12, 2)\) and perpendicular slope \(-1\):
\[
y - 2 = -1(x - 12)
\]
5. **Convert to slope-intercept form**:
\[
y - 2 = -x + 12 \implies y = -x + 14
\]
Thus, the equation of the line in slope-intercept form is \(y = -x + 14\).
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