Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 40SGR
Related questions
Question
![**Graph Analysis and Equation Completion**
**Graph Description:**
The graph provided is a linear graph plotted on a grid with labeled axes. The horizontal axis (x-axis) ranges from 0 to 5, while the vertical axis (y-axis) ranges from 0 to 30. The graph depicts a series of blue points connected by a straight blue line, illustrating a linear relationship between the two variables.
**Data Points:**
The specific coordinates of the points marked on the graph are as follows:
- (0, 25)
- (1, 20)
- (2, 15)
- (3, 10)
- (4, 5)
- (5, 0)
**Line Characteristics:**
The line has a negative slope, indicating that as the value of x increases, the value of y decreases. This is characteristic of a linear equation in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
**Task:**
Complete the equation for the graph provided.
**Instructions:**
Observe the graph to determine the slope (m) and the y-intercept (b). The line intersects the y-axis at y = 25, which is the y-intercept. By calculating the change in y over the change in x (rise over run), we find the slope \( m \).
\[ \text{Slope } (m) = \frac{\Delta y}{\Delta x} = \frac{25 - 20}{0 - 1} = \frac{-5}{1} = -5 \]
Hence, the equation of the line is:
\[ y = -5x + 25 \]
**Completing the Equation:**
Complete the equation for the graph:
\[ y = \_\_\_\_ \]
Based on our analysis, the complete equation is:
\[ y = -5x + 25 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84435934-315d-4f3f-bf89-3ba66c6d068b%2F3b67cf88-4cde-4b7d-9650-5882f3912d0c%2Fodxh3jc_processed.png&w=3840&q=75)
Transcribed Image Text:**Graph Analysis and Equation Completion**
**Graph Description:**
The graph provided is a linear graph plotted on a grid with labeled axes. The horizontal axis (x-axis) ranges from 0 to 5, while the vertical axis (y-axis) ranges from 0 to 30. The graph depicts a series of blue points connected by a straight blue line, illustrating a linear relationship between the two variables.
**Data Points:**
The specific coordinates of the points marked on the graph are as follows:
- (0, 25)
- (1, 20)
- (2, 15)
- (3, 10)
- (4, 5)
- (5, 0)
**Line Characteristics:**
The line has a negative slope, indicating that as the value of x increases, the value of y decreases. This is characteristic of a linear equation in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
**Task:**
Complete the equation for the graph provided.
**Instructions:**
Observe the graph to determine the slope (m) and the y-intercept (b). The line intersects the y-axis at y = 25, which is the y-intercept. By calculating the change in y over the change in x (rise over run), we find the slope \( m \).
\[ \text{Slope } (m) = \frac{\Delta y}{\Delta x} = \frac{25 - 20}{0 - 1} = \frac{-5}{1} = -5 \]
Hence, the equation of the line is:
\[ y = -5x + 25 \]
**Completing the Equation:**
Complete the equation for the graph:
\[ y = \_\_\_\_ \]
Based on our analysis, the complete equation is:
\[ y = -5x + 25 \]
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