### Understanding Slope and Y-InterceptThe 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.

Answered: Image /qna-images/answer/904387e9-bd25-4a6f-859c-129458d28088.jpg

Answered: y 9. -4 2. 6. -2 -4 slope m =…

Math

Algebra

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

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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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

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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.

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