**Transcription and Explanation for Educational Website**### Transcription**1. Write an equation, in slope-intercept form, for the line graphed below.**- The graph displays a line that intersects the y-axis at 5 and appears to have a negative slope, suggesting a decrease as the line moves from left to right.**2. Graph the line \( y = -2x + 3 \).****3. Graph the line \( y = \frac{4}{5}x + 2 \).****4. Write an equation, in slope-intercept form, for the line graphed below.**### Graph Descriptions and Analysis#### Diagram 1: Line Graph from Activity 1- The graph is presented on a coordinate plane with x-axis and y-axis both ranging from -6 to 6.- The plotted line starts from the point (0, 5) on the y-axis, indicating the y-intercept.- Points plotted on the line: (-3, 7), (0, 5), (3, 3).- The line shows a downward trend, indicating the slope is negative. For the given points, it seems the slope \( m \) can be calculated using the formula \( m = \frac{\Delta y}{\Delta x} \) between any two points.#### Diagram 2: Line Graph from Activity 3- Similarly presented on a coordinate plane from -6 to 6 on both axes.- The task involves graphing a line for the equation \( y = \frac{4}{5}x + 2 \).- To graph this, start at the y-intercept (0, 2) and use the slope \( \frac{4}{5} \) to identify another point by rising 4 units and running 5 units to the right.This transcription and analysis should help students understand how to interpret and create linear graphs using slope-intercept form. **Lesson on Graphing Lines and Slope-Intercept Form**1. **Graphing the Equation \( y = -2x + 3 \)** - **Objective:** To graph the linear equation \( y = -2x + 3 \). - **Equation Description:** This equation is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope \( m \) is -2, and the y-intercept \( b \) is 3. - **Graph Explanation:** - A grid is presented with x and y axes. The graph is centered at the origin (0,0) with axes extending from -6 to 6. - The line begins at the y-intercept, (0, 3), and descends with a slope of -2, meaning for each unit increase in x, y decreases by 2.2. **Writing an Equation for the Graphed Line** - **Objective:** To write the equation in slope-intercept form for the given line. - **Graph Description:** - The graph shows a line passing through points approximately at (0, -2) and (4, 2). - From these points, calculate the slope \( m = \frac{\Delta y}{\Delta x} = \frac{2 - (-2)}{4 - 0} = \frac{4}{4} = 1 \). - The y-intercept \( b \) is -2, as the line crosses the y-axis at (0, -2). - **Equation:** The equation of the line is \( y = x - 2 \).**Conclusion:** Understanding the components of a linear equation and plotting them accurately demonstrates how graphing works and highlights the relationship between algebraic representation and graphical interpretations.

Answered: Image /qna-images/answer/365a63a5-369f-48db-96a7-f9c7555e737a.jpg

1. Write an equation, in slope-intercept form, for the line graphed below. 3. Graph the line y =x+2 y 4 -6-5-4-3-2-1. 12 34 5 6 -6 -5-4-3-2-1, 1234 5 6 -2- -21 -3 -5+ -6 1. 2. Graph the line y = -2x+3 4. Write an equation, in slope-intercept form, for the line graphed below. 664 321 65 ENT 59 54 321

1. Write an equation, in slope-intercept form, for the line graphed below. 3. Graph the line y =x+2 y 4 -6-5-4-3-2-1. 12 34 5 6 -6 -5-4-3-2-1, 1234 5 6 -2- -21 -3 -5+ -6 1. 2. Graph the line y = -2x+3 4. Write an equation, in slope-intercept form, for the line graphed below. 664 321 65 ENT 59 54 321

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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Write the equation of the line in fully simplified slope-intercept form. 12 11 10 6. 2 1 1 2 3 4 5 6 7 8 9 10 11 12 -12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1, -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 Answer: Submit Answer
A. Find an equation of the line that satisfies the given conditions. Through (−1, −2) and (8, 7) B. Find an equation of the line that satisfies the given conditions. x-intercept −20, y-intercept 18

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