Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
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**Graph and Equation Explanation for Educational Purposes** ### Image Transcription: 1. **Equation:** - \( y = 2x - 1 \) - Presented in a linear form, indicating a straight line graph. 2. **Formula for Slope and Intercept:** - Slope = \(\frac{\text{rise}}{\text{run}}\) - \( y\)-intercept = \((0, b)\) which in this case refers to the constant in the equation. ### Diagram Details: **Graph:** - **Axes:** - **X-axis (horizontal):** Labeled with increments of 5, spanning from -5 to 5. - **Y-axis (vertical):** Labeled similarly to the X-axis with increments of 5, both positive and negative. - The central point of intersection is marked as \(O\). - **Grid:** - A square grid layout providing a coordinate plane for plotting. **Understanding the Graph:** - This graph is set up to plot the linear equation \( y = 2x - 1 \). - The slope of this line is 2, indicating it rises by 2 units for every 1 unit it moves horizontally to the right. - The y-intercept is -1, showing where the line crosses the y-axis. This setup is essential for understanding linear functions and how changes in slope and y-intercept affect the graph's position and orientation.
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Transcribed Image Text:**Graph and Equation Explanation for Educational Purposes** ### Image Transcription: 1. **Equation:** - \( y = 2x - 1 \) - Presented in a linear form, indicating a straight line graph. 2. **Formula for Slope and Intercept:** - Slope = \(\frac{\text{rise}}{\text{run}}\) - \( y\)-intercept = \((0, b)\) which in this case refers to the constant in the equation. ### Diagram Details: **Graph:** - **Axes:** - **X-axis (horizontal):** Labeled with increments of 5, spanning from -5 to 5. - **Y-axis (vertical):** Labeled similarly to the X-axis with increments of 5, both positive and negative. - The central point of intersection is marked as \(O\). - **Grid:** - A square grid layout providing a coordinate plane for plotting. **Understanding the Graph:** - This graph is set up to plot the linear equation \( y = 2x - 1 \). - The slope of this line is 2, indicating it rises by 2 units for every 1 unit it moves horizontally to the right. - The y-intercept is -1, showing where the line crosses the y-axis. This setup is essential for understanding linear functions and how changes in slope and y-intercept affect the graph's position and orientation.
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