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6. y = 3 x-y=-4 2. 21 1..

6. y = 3 x-y=-4 2. 21 1..

Advanced Engineering Mathematics
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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### Graphing Linear Equations **Equation 6:** - Given equations: - \( y = 3 \) - \( x - y = -4 \) #### Explanation of the Graph: The graph is a standard Cartesian coordinate plane with a visible grid, showing both positive and negative values along the x-axis and y-axis. Each axis is labeled with numbers ranging from -6 to 6. 1. **Equation \( y = 3 \):** - This is a horizontal line crossing the y-axis at \( y = 3 \). - On the graph, you would see a straight line parallel to the x-axis at the y-coordinate 3. 2. **Equation \( x - y = -4 \):** - Rearranging the equation gives \( y = x + 4 \). - This is a diagonal line with a positive slope, where the y-intercept is at (0, 4). - The line crosses the x-axis at (-4, 0) and rises slope upwards. In solving systems of equations graphically, the point where the two lines intersect would be the solution to the equation set. This representation helps visualize solutions and understand the relationships between the variables in linear equations.
Transcribed Image Text:### Graphing Linear Equations **Equation 6:** - Given equations: - \( y = 3 \) - \( x - y = -4 \) #### Explanation of the Graph: The graph is a standard Cartesian coordinate plane with a visible grid, showing both positive and negative values along the x-axis and y-axis. Each axis is labeled with numbers ranging from -6 to 6. 1. **Equation \( y = 3 \):** - This is a horizontal line crossing the y-axis at \( y = 3 \). - On the graph, you would see a straight line parallel to the x-axis at the y-coordinate 3. 2. **Equation \( x - y = -4 \):** - Rearranging the equation gives \( y = x + 4 \). - This is a diagonal line with a positive slope, where the y-intercept is at (0, 4). - The line crosses the x-axis at (-4, 0) and rises slope upwards. In solving systems of equations graphically, the point where the two lines intersect would be the solution to the equation set. This representation helps visualize solutions and understand the relationships between the variables in linear equations.
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