Graph the linear equation. y = 1 -x-- 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Instruction:**
Graph the linear equation.
**Equation:**
\[ y = -\frac{1}{5}x - 3 \]
**Explanation:**
This linear equation is in the slope-intercept form, \( y = mx + b \), where:
- \( m = -\frac{1}{5} \) is the slope.
- \( b = -3 \) is the y-intercept.
**Steps to Graph:**
1. **Plot the y-intercept:**
- Begin by plotting the point (0, -3) on the y-axis.
2. **Use the slope to find the next point:**
- The slope \(-\frac{1}{5}\) means for every 5 units you move to the right along the x-axis, move 1 unit down on the y-axis.
- From the y-intercept (0, -3), move 5 units to the right (to x = 5) and 1 unit down to locate the next point (5, -4).
3. **Draw the line:**
- Use a ruler to draw a straight line through the points (0, -3) and (5, -4). Extend the line across the graph.
This graph represents all solutions to the equation \( y = -\frac{1}{5}x - 3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F623b396d-263f-4ca9-bfd7-445804398e90%2F5c337a50-59e2-48d5-899b-d379c5490545%2Fh4nqcgf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction:**
Graph the linear equation.
**Equation:**
\[ y = -\frac{1}{5}x - 3 \]
**Explanation:**
This linear equation is in the slope-intercept form, \( y = mx + b \), where:
- \( m = -\frac{1}{5} \) is the slope.
- \( b = -3 \) is the y-intercept.
**Steps to Graph:**
1. **Plot the y-intercept:**
- Begin by plotting the point (0, -3) on the y-axis.
2. **Use the slope to find the next point:**
- The slope \(-\frac{1}{5}\) means for every 5 units you move to the right along the x-axis, move 1 unit down on the y-axis.
- From the y-intercept (0, -3), move 5 units to the right (to x = 5) and 1 unit down to locate the next point (5, -4).
3. **Draw the line:**
- Use a ruler to draw a straight line through the points (0, -3) and (5, -4). Extend the line across the graph.
This graph represents all solutions to the equation \( y = -\frac{1}{5}x - 3 \).
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