
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
![**Graphing Linear Equations: Example 1**
In this exercise, we are tasked with graphing the linear equation:
\[ 5x + y = 5 \]
### Steps to Graph the Equation
1. **Convert to Slope-Intercept Form:**
The equation can be rewritten in the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
\[ 5x + y = 5 \]
\[ y = -5x + 5 \]
Here, the slope \( m \) is \(-5\) and the y-intercept \( b \) is \(5\).
2. **Identify Key Points:**
- **Y-Intercept:** The y-intercept is the point where the line crosses the y-axis (\(y = 5\)).
- **X-Intercept:** Set \( y = 0 \) and solve for \( x \):
\[ 0 = -5x + 5 \]
\[ 5x = 5 \]
\[ x = 1 \]
So, the x-intercept is at \( (1, 0) \).
3. **Plot the Points:**
- Plot the y-intercept (0, 5) on the graph.
- Plot the x-intercept (1, 0) on the graph.
4. **Draw the Line:**
Connect these points with a straight line extending across the grid. This line represents the equation \( y = -5x + 5 \).
### Description of the Graph
The graph is drawn on a Cartesian coordinate system with both x and y axes ranging from -20 to 20. The graph should ideally show a straight line passing through the points (0, 5) and (1, 0), sloping downwards from left to right.
This exercise helps visualize how linear equations create straight lines, using intercepts and slopes to determine the line's position and direction on the graph.](https://content.bartleby.com/qna-images/question/e92e694a-8dce-4f5c-a0b3-7db66cedb1e5/eb972f7c-6dd1-4cdd-8c5f-89484291fb08/uhugizo.jpeg)
Transcribed Image Text:**Graphing Linear Equations: Example 1**
In this exercise, we are tasked with graphing the linear equation:
\[ 5x + y = 5 \]
### Steps to Graph the Equation
1. **Convert to Slope-Intercept Form:**
The equation can be rewritten in the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
\[ 5x + y = 5 \]
\[ y = -5x + 5 \]
Here, the slope \( m \) is \(-5\) and the y-intercept \( b \) is \(5\).
2. **Identify Key Points:**
- **Y-Intercept:** The y-intercept is the point where the line crosses the y-axis (\(y = 5\)).
- **X-Intercept:** Set \( y = 0 \) and solve for \( x \):
\[ 0 = -5x + 5 \]
\[ 5x = 5 \]
\[ x = 1 \]
So, the x-intercept is at \( (1, 0) \).
3. **Plot the Points:**
- Plot the y-intercept (0, 5) on the graph.
- Plot the x-intercept (1, 0) on the graph.
4. **Draw the Line:**
Connect these points with a straight line extending across the grid. This line represents the equation \( y = -5x + 5 \).
### Description of the Graph
The graph is drawn on a Cartesian coordinate system with both x and y axes ranging from -20 to 20. The graph should ideally show a straight line passing through the points (0, 5) and (1, 0), sloping downwards from left to right.
This exercise helps visualize how linear equations create straight lines, using intercepts and slopes to determine the line's position and direction on the graph.
![**Title: Understanding Intercepts in Graphs**
**Part 2 of 2**
In this section, you are tasked with identifying the x-intercepts and y-intercepts of a given graph. Each intercept should be written as an ordered pair.
- **x-intercept(s):** [ ]
- Input format: ( , )
- **y-intercept(s):** [ ]
- Input format: ( , )
A graphical interface allows you to enter intercepts, featuring boxes for user input and a cursor. A "Start Over" button is provided to clear entries and restart the task.
---
**How to Find Intercepts:**
- **x-intercept:** The point(s) where the graph crosses the x-axis. Here, y = 0.
- **y-intercept:** The point(s) where the graph crosses the y-axis. Here, x = 0.
Ensure that each intercept is accurately recorded as an ordered pair (x, y).
For further assistance or a step-by-step guide, feel free to reach out to your instructor or consult additional resources.](https://content.bartleby.com/qna-images/question/e92e694a-8dce-4f5c-a0b3-7db66cedb1e5/eb972f7c-6dd1-4cdd-8c5f-89484291fb08/1avhnhk.jpeg)
Transcribed Image Text:**Title: Understanding Intercepts in Graphs**
**Part 2 of 2**
In this section, you are tasked with identifying the x-intercepts and y-intercepts of a given graph. Each intercept should be written as an ordered pair.
- **x-intercept(s):** [ ]
- Input format: ( , )
- **y-intercept(s):** [ ]
- Input format: ( , )
A graphical interface allows you to enter intercepts, featuring boxes for user input and a cursor. A "Start Over" button is provided to clear entries and restart the task.
---
**How to Find Intercepts:**
- **x-intercept:** The point(s) where the graph crosses the x-axis. Here, y = 0.
- **y-intercept:** The point(s) where the graph crosses the y-axis. Here, x = 0.
Ensure that each intercept is accurately recorded as an ordered pair (x, y).
For further assistance or a step-by-step guide, feel free to reach out to your instructor or consult additional resources.
Expert Solution

arrow_forward
Step 1
Please see the answers below.
Step by stepSolved in 3 steps with 1 images

Knowledge Booster
Similar questions
- At the beginning of COVID- 19 Pandemic, the department of health used a graph to represent the prediction of the number of active cases and the horizontal axis shows the number of days since the start of the pandemic. Pennsylvanians residents were asked to quarantine to flatten the curve of the graph the represented the number of active infections. Which of the following statements are true? Select all the apply.arrow_forward3) Graph y - 20" a. 잘아! b. d.arrow_forwardUse the graph below to answer the questions. Identify whether each of the values below is positive, negative, or zero. Also, give a brief explanation of each of your answers. 1a). g'(-6) =? b). g'(2)=? c). g''(-6)=?arrow_forward
- 31 Whatis the value of expression shown below? 1.6 x 10 0.2 x 102 0.8 x 103 a8x 103 O 0.8 x 107 D 8 x 107arrow_forwardNumber 5arrow_forwardGraph 1 8- 6. 4- 2. Graph 2 Graph 3 -2- -6- • One-to-one? O Yes No O Yes No O Yes No Graph 4. Graph 5. Graph 6 4+ -8-64 -8- -6+ -8- -8-6-4 One-to-one? O Yes No O Yes No O Yes Noarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning

Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning