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30 25 20 >15 10 5 0 0 2 X 3 Complete the equation for the graph: y-0 4 5

30 25 20 >15 10 5 0 0 2 X 3 Complete the equation for the graph: y-0 4 5

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**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: \[ y = -5x + 25 \]
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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