Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 1E
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![### Problem Statement:
Find the slope-intercept form of the line satisfying the given conditions.
- **Condition:** Parallel to \(2x + 4y = 5\), passing through \((1,2)\).
---
### Question:
The slope-intercept form of the line parallel to \(2x + 4y = 5 \) passing through \((1,2)\) is \(\_\_\_\_\_\).
---
### Explanation:
To find the slope-intercept form \((y = mx + b)\) of the line, we need to follow these steps:
1. **Determine the slope of the given line:**
- The equation \(2x + 4y = 5\) can be rewritten in slope-intercept form:
\[
4y = -2x + 5 \\
y = -\frac{1}{2}x + \frac{5}{4}
\]
- From this equation, the slope \(m\) is \(-\frac{1}{2}\).
2. **Use the slope for the new line:**
- The line we are looking for is parallel to the given line, so it will have the same slope \(m = -\frac{1}{2}\).
3. **Find the y-intercept using the given point \((1,2)\):**
- Substitute \((x, y) = (1, 2)\) and \(m = -\frac{1}{2}\) into the slope-intercept form \(y = mx + b\):
\[
2 = -\frac{1}{2}(1) + b \\
2 = -\frac{1}{2} + b \\
b = 2 + \frac{1}{2} \\
b = \frac{4}{2} + \frac{1}{2} \\
b = \frac{5}{2}
\]
4. **Write the equation:**
- Substituting \(m = -\frac{1}{2}\) and \(b = \frac{5}{2}\) into the equation \(y = mx + b\):
\[
y = -\frac{1}{2}x + \frac{5}{2}
\]
So, the slope-intercept form of the line parallel](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F375a8daa-a061-40df-aa13-f324a3b06fab%2Fac800253-6378-479a-991e-aa5480b0fd03%2F63nnq7_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Find the slope-intercept form of the line satisfying the given conditions.
- **Condition:** Parallel to \(2x + 4y = 5\), passing through \((1,2)\).
---
### Question:
The slope-intercept form of the line parallel to \(2x + 4y = 5 \) passing through \((1,2)\) is \(\_\_\_\_\_\).
---
### Explanation:
To find the slope-intercept form \((y = mx + b)\) of the line, we need to follow these steps:
1. **Determine the slope of the given line:**
- The equation \(2x + 4y = 5\) can be rewritten in slope-intercept form:
\[
4y = -2x + 5 \\
y = -\frac{1}{2}x + \frac{5}{4}
\]
- From this equation, the slope \(m\) is \(-\frac{1}{2}\).
2. **Use the slope for the new line:**
- The line we are looking for is parallel to the given line, so it will have the same slope \(m = -\frac{1}{2}\).
3. **Find the y-intercept using the given point \((1,2)\):**
- Substitute \((x, y) = (1, 2)\) and \(m = -\frac{1}{2}\) into the slope-intercept form \(y = mx + b\):
\[
2 = -\frac{1}{2}(1) + b \\
2 = -\frac{1}{2} + b \\
b = 2 + \frac{1}{2} \\
b = \frac{4}{2} + \frac{1}{2} \\
b = \frac{5}{2}
\]
4. **Write the equation:**
- Substituting \(m = -\frac{1}{2}\) and \(b = \frac{5}{2}\) into the equation \(y = mx + b\):
\[
y = -\frac{1}{2}x + \frac{5}{2}
\]
So, the slope-intercept form of the line parallel
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