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(547) m=2, Point (-3,-1)

(547) m=2, Point (-3,-1)

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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Please Answer 547,552
### Chapter 3 **Problem 539:** Find the slope of the line between the points (5, 2) and (-1, -4). \[ m = \frac{2 - (-4)}{5 - (-1)} = \frac{2 + 4}{5 + 1} = \frac{6}{6} = 1 \] **Problem 540:** Graph the line with slope \(\frac{3}{5}\) using the point (0, -1). Equation derived from point-slope form: \[ y + 1 = -\frac{3}{5}(x - 0) \] Simplified to slope-intercept form: \[ y = -\frac{3}{5}x - 1 \] **Graph Explanation:** The image contains two coordinate plane graphs: - **Graph on the left**: Displays a line drawn through points, illustrating the equation \( y = -\frac{3}{5}x - 1 \). - **Graph on the right**: Displaying a coordinate plane with axes marked from -6 to 6 on both x and y-axes but without additional details. **Problem 541:** Graph the line with slope \(\frac{1}{2}\) containing the point (-3, -4).
Transcribed Image Text:### Chapter 3 **Problem 539:** Find the slope of the line between the points (5, 2) and (-1, -4). \[ m = \frac{2 - (-4)}{5 - (-1)} = \frac{2 + 4}{5 + 1} = \frac{6}{6} = 1 \] **Problem 540:** Graph the line with slope \(\frac{3}{5}\) using the point (0, -1). Equation derived from point-slope form: \[ y + 1 = -\frac{3}{5}(x - 0) \] Simplified to slope-intercept form: \[ y = -\frac{3}{5}x - 1 \] **Graph Explanation:** The image contains two coordinate plane graphs: - **Graph on the left**: Displays a line drawn through points, illustrating the equation \( y = -\frac{3}{5}x - 1 \). - **Graph on the right**: Displaying a coordinate plane with axes marked from -6 to 6 on both x and y-axes but without additional details. **Problem 541:** Graph the line with slope \(\frac{1}{2}\) containing the point (-3, -4).
### Mathematics: Graphs from Text #### Item 547 Given: - Slope (\(m\)): 2 - Point: \((-3, -1)\) This information can be used to form the equation of a line using the point-slope formula: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the point \((-3, -1)\). #### Item 552 Inequality: \[ x - y \geq -4 \] This represents a linear inequality. The line \( x - y = -4 \) can be graphed, and the solution to the inequality includes the shaded region above and including the line.
Transcribed Image Text:### Mathematics: Graphs from Text #### Item 547 Given: - Slope (\(m\)): 2 - Point: \((-3, -1)\) This information can be used to form the equation of a line using the point-slope formula: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the point \((-3, -1)\). #### Item 552 Inequality: \[ x - y \geq -4 \] This represents a linear inequality. The line \( x - y = -4 \) can be graphed, and the solution to the inequality includes the shaded region above and including the line.
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