Write an equation of the line that passes through (2.5, -3.8) and is perpendicular to the line defined by 5x=3-y. Write the answer in slope- intercept form (if possible) and in standard form (Ax+By = C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable. Part: 0/2
Write an equation of the line that passes through (2.5, -3.8) and is perpendicular to the line defined by 5x=3-y. Write the answer in slope- intercept form (if possible) and in standard form (Ax+By = C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable. Part: 0/2
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Topic: Writing Equations of Perpendicular Lines**
### Problem:
Write an equation of the line that passes through (2.5, -3.8) and is perpendicular to the line defined by \(5x = 3 - y\). Write the answer in slope-intercept form (if possible) and in standard form (\(Ax + By = C\)) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
**Part: 0 / 2**
#### Part 1 of 2
**Task:**
The equation of the line in slope-intercept form:
**Options:**
[Input box] \(\square \)
Checkbox: [ ] Cannot be written
**Action Buttons:**
- **Skip Part**
- **Check**
- **Save For Later**
- **Submit Assignment**
---
#### Explanation:
To solve this problem, we need to:
1. **Determine the slope of the given line:**
The given line equation is \(5x = 3 - y\). First, we rearrange it into slope-intercept form \(y = mx + b\).
\[
y = -5x + 3
\]
So, the slope \(m_{\text{given}}\) of the given line is \(-5\).
2. **Find the slope of the perpendicular line:**
Perpendicular lines have slopes that are negative reciprocals of each other.
\[
m_{\text{perpendicular}} = \frac{1}{5}
\]
3. **Use the slope-intercept form equation:**
Use the point-slope form equation \( (y - y_1 = m(x - x_1)) \) with the point \((2.5, -3.8)\) and slope \(\frac{1}{5}\).
\[
y + 3.8 = \frac{1}{5}(x - 2.5)
\]
4. **Convert to slope-intercept form:**
\[
y + 3.8 = \frac{1}{5}x - \frac{2.5}{5}
\]
\[
y + 3.8 = \frac{1}{5}x - 0.5
\]
\[
y = \frac{1}{5}x - 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98398fcd-aa3b-4aac-8dda-e0ea37100738%2F05c5609e-152f-4a19-87cf-8345962c3b30%2Fj4krei_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Writing Equations of Perpendicular Lines**
### Problem:
Write an equation of the line that passes through (2.5, -3.8) and is perpendicular to the line defined by \(5x = 3 - y\). Write the answer in slope-intercept form (if possible) and in standard form (\(Ax + By = C\)) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
**Part: 0 / 2**
#### Part 1 of 2
**Task:**
The equation of the line in slope-intercept form:
**Options:**
[Input box] \(\square \)
Checkbox: [ ] Cannot be written
**Action Buttons:**
- **Skip Part**
- **Check**
- **Save For Later**
- **Submit Assignment**
---
#### Explanation:
To solve this problem, we need to:
1. **Determine the slope of the given line:**
The given line equation is \(5x = 3 - y\). First, we rearrange it into slope-intercept form \(y = mx + b\).
\[
y = -5x + 3
\]
So, the slope \(m_{\text{given}}\) of the given line is \(-5\).
2. **Find the slope of the perpendicular line:**
Perpendicular lines have slopes that are negative reciprocals of each other.
\[
m_{\text{perpendicular}} = \frac{1}{5}
\]
3. **Use the slope-intercept form equation:**
Use the point-slope form equation \( (y - y_1 = m(x - x_1)) \) with the point \((2.5, -3.8)\) and slope \(\frac{1}{5}\).
\[
y + 3.8 = \frac{1}{5}(x - 2.5)
\]
4. **Convert to slope-intercept form:**
\[
y + 3.8 = \frac{1}{5}x - \frac{2.5}{5}
\]
\[
y + 3.8 = \frac{1}{5}x - 0.5
\]
\[
y = \frac{1}{5}x - 0.
![**Write an Equation of a Line (Educational Exercise)**
**Problem Statement:**
Write an equation of the line that passes through \((-5, -1)\) and is parallel to the line defined by \(5x + y = 4\). Write the answer in slope-intercept form (if possible) and in standard form \((Ax + By = C)\) with the smallest integer coefficients. Use the "Cannot be written" button, if applicable.
**Progress Indicator:**
Part: **0 / 2**
**Part 1 of 2:**
- **The equation of the line in slope-intercept form:**
- Input Field: [ ]
- Options:
- \( \square \) Cannot be written
**Action Buttons:**
- Skip Part
- Check
- (Click this button to verify your answer)
- Save For Later
- Submit All
**Footer:**
© 2022 McGraw Hill LLC. All Rights Reserved.
- Terms of Use
- Privacy Center
---
**Explanation**:
This exercise tests the ability to write equations of lines based on given conditions. Specifically, it involves writing equations in both slope-intercept form \((y = mx + b)\) and standard form \((Ax + By = C)\) for lines that pass through a particular point and are parallel to a given line. The student is advised to use a button indicating that a form "Cannot be written" if they find it impossible to achieve the form with given constraints.
**Steps to Solve:**
1. Identify the slope of the given line (\(5x + y = 4\)).
2. Use the point \((-5, -1)\) and the identified slope to determine the equation in slope-intercept form.
3. Convert the slope-intercept form to standard form with the smallest integer coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98398fcd-aa3b-4aac-8dda-e0ea37100738%2F05c5609e-152f-4a19-87cf-8345962c3b30%2Fd50yqs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Write an Equation of a Line (Educational Exercise)**
**Problem Statement:**
Write an equation of the line that passes through \((-5, -1)\) and is parallel to the line defined by \(5x + y = 4\). Write the answer in slope-intercept form (if possible) and in standard form \((Ax + By = C)\) with the smallest integer coefficients. Use the "Cannot be written" button, if applicable.
**Progress Indicator:**
Part: **0 / 2**
**Part 1 of 2:**
- **The equation of the line in slope-intercept form:**
- Input Field: [ ]
- Options:
- \( \square \) Cannot be written
**Action Buttons:**
- Skip Part
- Check
- (Click this button to verify your answer)
- Save For Later
- Submit All
**Footer:**
© 2022 McGraw Hill LLC. All Rights Reserved.
- Terms of Use
- Privacy Center
---
**Explanation**:
This exercise tests the ability to write equations of lines based on given conditions. Specifically, it involves writing equations in both slope-intercept form \((y = mx + b)\) and standard form \((Ax + By = C)\) for lines that pass through a particular point and are parallel to a given line. The student is advised to use a button indicating that a form "Cannot be written" if they find it impossible to achieve the form with given constraints.
**Steps to Solve:**
1. Identify the slope of the given line (\(5x + y = 4\)).
2. Use the point \((-5, -1)\) and the identified slope to determine the equation in slope-intercept form.
3. Convert the slope-intercept form to standard form with the smallest integer coefficients.
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