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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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![**Title: Writing and Graphing Linear Equations**
**Objective:**
Convert an English sentence into a mathematical equation with two variables and graph the equation.
**Sentence to Equation:**
"The y-value is five more than three times the x-value."
**Mathematical Representation:**
To express this sentence as an equation, let \( y \) represent the y-value and \( x \) represent the x-value. The equation becomes:
\[ y = 3x + 5 \]
**Graphing Instructions:**
1. **Understanding the Equation:** The equation \( y = 3x + 5 \) is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope (3) and \( b \) is the y-intercept (5).
2. **Plot the Y-intercept:** Begin by placing a point on the y-axis at (0, 5), the y-intercept.
3. **Use the Slope:** From the y-intercept, use the slope to find another point. A slope of 3 means rise 3 units up for every 1 unit moved to the right. From (0, 5), move to (1, 8).
4. **Draw the Line:** Connect the two points with a straight line extending in both directions.
**Graph Description:**
The provided graph is a standard Cartesian coordinate grid:
- The x-axis ranges from -10 to 8.
- The y-axis ranges from -8 to 10.
- Both axes have markings for each integer value.
- The graph tool allows you to click and enlarge for more precise graphing.
By following these steps, you can accurately graph the equation and visualize the linear relationship between \( x \) and \( y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffebfc829-3adc-4601-a5b5-bd5b3e3c23b0%2Fadca4689-26bf-4ec2-8b73-c0c96557ba4f%2Faxim2b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Writing and Graphing Linear Equations**
**Objective:**
Convert an English sentence into a mathematical equation with two variables and graph the equation.
**Sentence to Equation:**
"The y-value is five more than three times the x-value."
**Mathematical Representation:**
To express this sentence as an equation, let \( y \) represent the y-value and \( x \) represent the x-value. The equation becomes:
\[ y = 3x + 5 \]
**Graphing Instructions:**
1. **Understanding the Equation:** The equation \( y = 3x + 5 \) is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope (3) and \( b \) is the y-intercept (5).
2. **Plot the Y-intercept:** Begin by placing a point on the y-axis at (0, 5), the y-intercept.
3. **Use the Slope:** From the y-intercept, use the slope to find another point. A slope of 3 means rise 3 units up for every 1 unit moved to the right. From (0, 5), move to (1, 8).
4. **Draw the Line:** Connect the two points with a straight line extending in both directions.
**Graph Description:**
The provided graph is a standard Cartesian coordinate grid:
- The x-axis ranges from -10 to 8.
- The y-axis ranges from -8 to 10.
- Both axes have markings for each integer value.
- The graph tool allows you to click and enlarge for more precise graphing.
By following these steps, you can accurately graph the equation and visualize the linear relationship between \( x \) and \( y \).
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