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,...
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Question
![**Title: Writing the Equation of a Parallel Line**
**Objective:**
Learn how to find the equation of a line given a point and a parallel line.
**Problem Statement:**
Write the equation of the line with the given information:
- Passes through the point \((-5, 6)\)
- Parallel to the line \(h(x) = -1x + 5\)
**Equation Form:**
The general form of a linear equation is \(y = mx + b\), where:
- \(m\) is the slope
- \(b\) is the y-intercept
**Given Information:**
1. The given line \(h(x) = -1x + 5\) has a slope \(m = -1\).
2. Lines that are parallel have identical slopes.
**Steps to Solve:**
1. **Identify the Slope:**
Since the line is parallel to \(h(x)\), the slope of the new line is also \(-1\).
2. **Use the Point-Slope Formula:**
The point-slope formula is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a given point on the line.
3. **Substitute the Values:**
- Substitute the slope \(m = -1\).
- Insert the point \((-5, 6)\) into the formula.
\[
y - 6 = -1(x + 5)
\]
4. **Simplify:**
\[
y - 6 = -1x - 5
\]
\[
y = -x + 1
\]
**Equation of the Line:**
The equation of the line is \(f(x) = -x + 1\). This line passes through the point \((-5, 6)\) and is parallel to \(h(x) = -1x + 5\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96220fd0-c27e-43c2-93ca-a13fa452ca67%2Fa0b13ede-0468-451c-8a3c-65d988335c8f%2Fi47n0fj_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Writing the Equation of a Parallel Line**
**Objective:**
Learn how to find the equation of a line given a point and a parallel line.
**Problem Statement:**
Write the equation of the line with the given information:
- Passes through the point \((-5, 6)\)
- Parallel to the line \(h(x) = -1x + 5\)
**Equation Form:**
The general form of a linear equation is \(y = mx + b\), where:
- \(m\) is the slope
- \(b\) is the y-intercept
**Given Information:**
1. The given line \(h(x) = -1x + 5\) has a slope \(m = -1\).
2. Lines that are parallel have identical slopes.
**Steps to Solve:**
1. **Identify the Slope:**
Since the line is parallel to \(h(x)\), the slope of the new line is also \(-1\).
2. **Use the Point-Slope Formula:**
The point-slope formula is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a given point on the line.
3. **Substitute the Values:**
- Substitute the slope \(m = -1\).
- Insert the point \((-5, 6)\) into the formula.
\[
y - 6 = -1(x + 5)
\]
4. **Simplify:**
\[
y - 6 = -1x - 5
\]
\[
y = -x + 1
\]
**Equation of the Line:**
The equation of the line is \(f(x) = -x + 1\). This line passes through the point \((-5, 6)\) and is parallel to \(h(x) = -1x + 5\).
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