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Find an equation for each line. Equation for line k: M 6 -4 -3 -2 4 N 4 -~ tol 40 r +

Find an equation for each line. Equation for line k: M 6 -4 -3 -2 4 N 4 -~ tol 40 r +

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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## Finding Equations of Lines ### Instructions: - Find an equation for each line depicted on the graph. ### Graph Description: The graph is a standard Cartesian coordinate plane with two lines plotted on it, labeled as line \( m \) and line \( k \). #### Key Points: - **Line \( m \)**: - Appears to intersect the vertical axis (y-axis) at point \( (0,4) \). - Also crosses the horizontal axis (x-axis) at point \( (-4,0) \). - **Line \( k \)**: - Intersects the vertical axis (y-axis) at point \( (0,6) \). - Crosses the horizontal axis (x-axis) at point \( (3,0) \). #### Slope Calculation: - **Line \( m \)**: - Slope = Rise/Run = \((4 - 0) / (0 + 4) = 4/4 = 1\). - Slope-intercept form is \( y = mx + b \), thus the equation is \( y = x + 4 \). - **Line \( k \)**: - Slope = Rise/Run = \((6 - 0) / (0 - 3) = 6/-3 = -2\). - Slope-intercept form is \( y = mx + b \), thus the equation is \( y = -2x + 6 \). ### Conclusion: - Write the equation for Line \( k \) based on the slope-intercept form determined. **Equation for line \( k \):** \( y = -2x + 6 \)
Transcribed Image Text:## Finding Equations of Lines ### Instructions: - Find an equation for each line depicted on the graph. ### Graph Description: The graph is a standard Cartesian coordinate plane with two lines plotted on it, labeled as line \( m \) and line \( k \). #### Key Points: - **Line \( m \)**: - Appears to intersect the vertical axis (y-axis) at point \( (0,4) \). - Also crosses the horizontal axis (x-axis) at point \( (-4,0) \). - **Line \( k \)**: - Intersects the vertical axis (y-axis) at point \( (0,6) \). - Crosses the horizontal axis (x-axis) at point \( (3,0) \). #### Slope Calculation: - **Line \( m \)**: - Slope = Rise/Run = \((4 - 0) / (0 + 4) = 4/4 = 1\). - Slope-intercept form is \( y = mx + b \), thus the equation is \( y = x + 4 \). - **Line \( k \)**: - Slope = Rise/Run = \((6 - 0) / (0 - 3) = 6/-3 = -2\). - Slope-intercept form is \( y = mx + b \), thus the equation is \( y = -2x + 6 \). ### Conclusion: - Write the equation for Line \( k \) based on the slope-intercept form determined. **Equation for line \( k \):** \( y = -2x + 6 \)
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