Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.2: Writing Equations In Standard And Point-slope Forms
Problem 1CYU
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Please, can I get readable handwriting?
![The image consists of a graphical representation combined with a mathematical equation used to find the shaded area on the graph. Follow the details below for educational purposes:
### Understanding the Graph and Calculation
#### Graph Explanation:
The graph presented is a coordinate plane with a line intersecting the y-axis at 5 and the x-axis at 5, forming a right triangle with the axes. There is a blue shaded region between the x-coordinates 1 and 2 under the line.
#### Mathematical Calculation:
To find the blue shaded area between x=1 and x=2 under the curve (which in this case is a straight line), we use the following integral calculation:
\[ \int_{a}^{b} f(x) \, dx = \text{area} \]
Where:
- \( a \) and \( b \) are the lower and upper bounds of the shaded region along the x-axis.
- \( f(x) \) is the function representing the line.
- The integral calculates the area under the curve from \( a \) to \( b \).
##### Parameters to be identified:
- \( a \) = \_\_\_\_
- \( b \) = \_\_\_\_
- \( f(x) \) = \_\_\_\_
- Area = \_\_\_\_
For the given graph:
- \( a \) (the lower bound) should be identified.
- \( b \) (the upper bound) should be identified.
- \( f(x) \) is the equation of the line.
To find the blue shaded area, you need to identify the function \( f(x) \), set the bounds \( a \) and \( b \), and compute the integral accordingly.
### Steps to Compute:
1. **Identify \( a \) and \( b \):**
- \( a \) = 1 (the left boundary of the blue region)
- \( b \) = 2 (the right boundary of the blue region)
2. **Determine \( f(x) \), the equation of the line:**
- By inspecting the graph, the line passes through (0, 5) and (5, 0). This suggests a slope of -1. Hence, the equation \( f(x) \) can be written as:
\[ f(x) = -x + 5 \]
3. **Calculate the area using the integral:**
- Substitute \( a \), \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F469aef3b-31ef-41c9-aa0d-266ee90c84d9%2F6cdb6414-ea58-49ae-b0a5-e8dfa24edaa8%2Fui223f_processed.png&w=3840&q=75)
Transcribed Image Text:The image consists of a graphical representation combined with a mathematical equation used to find the shaded area on the graph. Follow the details below for educational purposes:
### Understanding the Graph and Calculation
#### Graph Explanation:
The graph presented is a coordinate plane with a line intersecting the y-axis at 5 and the x-axis at 5, forming a right triangle with the axes. There is a blue shaded region between the x-coordinates 1 and 2 under the line.
#### Mathematical Calculation:
To find the blue shaded area between x=1 and x=2 under the curve (which in this case is a straight line), we use the following integral calculation:
\[ \int_{a}^{b} f(x) \, dx = \text{area} \]
Where:
- \( a \) and \( b \) are the lower and upper bounds of the shaded region along the x-axis.
- \( f(x) \) is the function representing the line.
- The integral calculates the area under the curve from \( a \) to \( b \).
##### Parameters to be identified:
- \( a \) = \_\_\_\_
- \( b \) = \_\_\_\_
- \( f(x) \) = \_\_\_\_
- Area = \_\_\_\_
For the given graph:
- \( a \) (the lower bound) should be identified.
- \( b \) (the upper bound) should be identified.
- \( f(x) \) is the equation of the line.
To find the blue shaded area, you need to identify the function \( f(x) \), set the bounds \( a \) and \( b \), and compute the integral accordingly.
### Steps to Compute:
1. **Identify \( a \) and \( b \):**
- \( a \) = 1 (the left boundary of the blue region)
- \( b \) = 2 (the right boundary of the blue region)
2. **Determine \( f(x) \), the equation of the line:**
- By inspecting the graph, the line passes through (0, 5) and (5, 0). This suggests a slope of -1. Hence, the equation \( f(x) \) can be written as:
\[ f(x) = -x + 5 \]
3. **Calculate the area using the integral:**
- Substitute \( a \), \(
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