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
Need help, please do it as showen in textbook
![**Task: Find an Equation of a Perpendicular Line**
**Problem Statement:**
Write an equation for a line perpendicular to \( y = -4x + 5 \) and passing through the point \((-8, -3)\).
**Solution Steps:**
1. **Identify the Slope of the Given Line:**
- The equation of the given line is \( y = -4x + 5 \), which is in slope-intercept form \( y = mx + b \).
- The slope (\(m\)) of this line is \(-4\).
2. **Determine the Slope of the Perpendicular Line:**
- The slope of a line perpendicular to another is the negative reciprocal.
- Therefore, the slope of the line perpendicular to \( y = -4x + 5 \) is \(\frac{1}{4}\).
3. **Use the Point-Slope Form to Write the Equation:**
- The point-slope form of a line is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope, and \((x_1, y_1)\) is a point on the line.
- Using the point \((-8, -3)\) and slope \(\frac{1}{4}\), the equation becomes:
\[
y - (-3) = \frac{1}{4}(x - (-8))
\]
\[
y + 3 = \frac{1}{4}(x + 8)
\]
4. **Simplify to Slope-Intercept Form \( y = mx + b \):**
- Distribute the slope on the right side:
\[
y + 3 = \frac{1}{4}x + 2
\]
- Subtract 3 from both sides to solve for \( y \):
\[
y = \frac{1}{4}x + 2 - 3
\]
\[
y = \frac{1}{4}x - 1
\]
**Final Answer:**
The equation of the line perpendicular to \( y = -4x + 5 \) and passing through the point \((-8, -3)\) is:
\[
y = \frac{1}{4}x - 1
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d656125-4418-43a7-9497-1ff8e92c92dc%2F5e9319ed-f979-42eb-acaf-9f96c96c23c2%2Fmt420p_processed.png&w=3840&q=75)
Transcribed Image Text:**Task: Find an Equation of a Perpendicular Line**
**Problem Statement:**
Write an equation for a line perpendicular to \( y = -4x + 5 \) and passing through the point \((-8, -3)\).
**Solution Steps:**
1. **Identify the Slope of the Given Line:**
- The equation of the given line is \( y = -4x + 5 \), which is in slope-intercept form \( y = mx + b \).
- The slope (\(m\)) of this line is \(-4\).
2. **Determine the Slope of the Perpendicular Line:**
- The slope of a line perpendicular to another is the negative reciprocal.
- Therefore, the slope of the line perpendicular to \( y = -4x + 5 \) is \(\frac{1}{4}\).
3. **Use the Point-Slope Form to Write the Equation:**
- The point-slope form of a line is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope, and \((x_1, y_1)\) is a point on the line.
- Using the point \((-8, -3)\) and slope \(\frac{1}{4}\), the equation becomes:
\[
y - (-3) = \frac{1}{4}(x - (-8))
\]
\[
y + 3 = \frac{1}{4}(x + 8)
\]
4. **Simplify to Slope-Intercept Form \( y = mx + b \):**
- Distribute the slope on the right side:
\[
y + 3 = \frac{1}{4}x + 2
\]
- Subtract 3 from both sides to solve for \( y \):
\[
y = \frac{1}{4}x + 2 - 3
\]
\[
y = \frac{1}{4}x - 1
\]
**Final Answer:**
The equation of the line perpendicular to \( y = -4x + 5 \) and passing through the point \((-8, -3)\) is:
\[
y = \frac{1}{4}x - 1
\]
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education