Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
**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.
Transcribed Image Text:**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.
Transcribed Image Text:**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.
Expert Solution
Step 1

Advanced Math homework question answer, step 1, image 1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS