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y 9. -4 2. 6. -2 -4 slope m = y-intercept b = 4, 2.

y 9. -4 2. 6. -2 -4 slope m = y-intercept b = 4, 2.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Understanding Slope and Y-Intercept The task involves analyzing the given graph to determine the slope and y-intercept of the line. #### Graph Description - The graph is a standard Cartesian plane with the x-axis and y-axis intersecting at the origin (0,0). - The x-axis ranges from -6 to 6, and the y-axis ranges from -6 to 6. - A straight line passes through the graph with a positive slope. #### Important Points to Note - The line crosses the y-axis at (0,2). This point is the y-intercept of the line. - The line also passes through the point (-2,0) on the x-axis. #### Calculating the Slope (m) Slope is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Taking two points from the graph: - Point 1: (0, 2) - Point 2: (-2, 0) Substitute these into the formula: \[ m = \frac{0 - 2}{-2 - 0} = \frac{-2}{-2} = 1 \] The slope \( m \) is 1. #### Identifying the Y-Intercept (b) - The y-intercept is the point where the line crosses the y-axis. - From the graph, this occurs at (0, 2), so the y-intercept \( b \) is 2. #### Summary - **Slope \( m \) = 1** - **Y-intercept \( b \) = 2** This analysis of the graph concludes with the identification of the line’s slope and y-intercept, essential for understanding linear equations.
Transcribed Image Text:### Understanding Slope and Y-Intercept The task involves analyzing the given graph to determine the slope and y-intercept of the line. #### Graph Description - The graph is a standard Cartesian plane with the x-axis and y-axis intersecting at the origin (0,0). - The x-axis ranges from -6 to 6, and the y-axis ranges from -6 to 6. - A straight line passes through the graph with a positive slope. #### Important Points to Note - The line crosses the y-axis at (0,2). This point is the y-intercept of the line. - The line also passes through the point (-2,0) on the x-axis. #### Calculating the Slope (m) Slope is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Taking two points from the graph: - Point 1: (0, 2) - Point 2: (-2, 0) Substitute these into the formula: \[ m = \frac{0 - 2}{-2 - 0} = \frac{-2}{-2} = 1 \] The slope \( m \) is 1. #### Identifying the Y-Intercept (b) - The y-intercept is the point where the line crosses the y-axis. - From the graph, this occurs at (0, 2), so the y-intercept \( b \) is 2. #### Summary - **Slope \( m \) = 1** - **Y-intercept \( b \) = 2** This analysis of the graph concludes with the identification of the line’s slope and y-intercept, essential for understanding linear equations.
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