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What are the coordinates of point C: (x, y) = (2 14 ) What are the coordinates of point E: (x, y) = (4 , 3 ) Based on these two points, what is the slope of the line? Slope =

What are the coordinates of point C: (x, y) = (2 14 ) What are the coordinates of point E: (x, y) = (4 , 3 ) Based on these two points, what is the slope of the line? Slope =

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter7: Equations And Inequalities In Two Variables
Section7.1: Rectangular Coordinate System And Linear Equations
Problem 43PS
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### Understanding Coordinates on a Graph The graph provided represents a Cartesian coordinate system with points labeled A, B, C, D, and E. These points lie on a straight line which indicates a linear relationship between the x and y coordinates. #### Explanation of the Graph: - The x-axis is labeled as "X," ranging from 0 to 5. - The y-axis is labeled as "Y," ranging from 0 to 30. - Points A, B, C, D, and E are plotted and connected by a blue line, indicating a negative slope. ### Questions: 1. **What are the coordinates of point C:** - \( (x, y) = ( \_\_\_ , \_\_\_ ) \) - Answer: \( (x, y) = (2, 14) \) 2. **What are the coordinates of point E:** - \( (x, y) = ( \_\_\_ , \_\_\_ ) \) - Answer: \( (x, y) = (4, 3) \) 3. **Based on these two points, what is the slope of the line?** - **Slope Calculation Formula:** \[ \text{Slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \] - Using points C \((2, 14)\) and E \((4, 3)\): \[ \text{Slope} (m) = \frac{3 - 14}{4 - 2} = \frac{-11}{2} \] - **Slope =** \( -5.5 \) ### Summary: - **Point C coordinates:** \( (2, 14) \) - **Point E coordinates:** \( (4, 3) \) - **Slope of the line:** \( -5.5 \) ### Visual Aid: - **Graph Description:** The graph demonstrates how to identify coordinates and calculate the slope of a line based on selected points. Point C is at (2, 14) and Point E is at (4, 3). Observing and locating these points on the graph helps in visual understanding and practical calculations of slope. This exercise is crucial for understanding linear relationships and how coordinates are used in geometry and algebra.
Transcribed Image Text:### Understanding Coordinates on a Graph The graph provided represents a Cartesian coordinate system with points labeled A, B, C, D, and E. These points lie on a straight line which indicates a linear relationship between the x and y coordinates. #### Explanation of the Graph: - The x-axis is labeled as "X," ranging from 0 to 5. - The y-axis is labeled as "Y," ranging from 0 to 30. - Points A, B, C, D, and E are plotted and connected by a blue line, indicating a negative slope. ### Questions: 1. **What are the coordinates of point C:** - \( (x, y) = ( \_\_\_ , \_\_\_ ) \) - Answer: \( (x, y) = (2, 14) \) 2. **What are the coordinates of point E:** - \( (x, y) = ( \_\_\_ , \_\_\_ ) \) - Answer: \( (x, y) = (4, 3) \) 3. **Based on these two points, what is the slope of the line?** - **Slope Calculation Formula:** \[ \text{Slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \] - Using points C \((2, 14)\) and E \((4, 3)\): \[ \text{Slope} (m) = \frac{3 - 14}{4 - 2} = \frac{-11}{2} \] - **Slope =** \( -5.5 \) ### Summary: - **Point C coordinates:** \( (2, 14) \) - **Point E coordinates:** \( (4, 3) \) - **Slope of the line:** \( -5.5 \) ### Visual Aid: - **Graph Description:** The graph demonstrates how to identify coordinates and calculate the slope of a line based on selected points. Point C is at (2, 14) and Point E is at (4, 3). Observing and locating these points on the graph helps in visual understanding and practical calculations of slope. This exercise is crucial for understanding linear relationships and how coordinates are used in geometry and algebra.
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