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,...
Related questions
Question
![**Title:** Understanding the Slope of a Line
**Introduction:**
In this section, we will explore how to find the slope of a line using a graph.
**Graph Description:**
The graph provided displays a straight line plotted on a coordinate grid. The line slopes downward from the left to the right, crossing both the vertical (y-axis) and horizontal (x-axis) axes.
**Identifying Slope:**
1. **Identify Two Points:**
- The line intersects grid lines at two visible points. These points can be used to calculate the line's slope.
2. **Calculate Slope (m):**
- The slope \( m \) is determined by the formula:
\[
m = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}}
\]
- **Rise:** The change in the vertical direction (y-axis).
- **Run:** The change in the horizontal direction (x-axis).
3. **Example Calculation:**
- Find the vertical change (rise) between two points.
- Find the horizontal change (run) between the same points.
- Insert the values into the slope formula to find \( m \).
**Conclusion:**
The graph aids in visualizing how the slope represents the steepness and direction of a line. Calculating the slope is crucial in understanding linear relationships in algebra.
**Problem:**
Calculate the slope \( m \) for the given line using the graph.
---
Use this guide to understand how to determine the slope of any given line on a graph by visually identifying points and using the slope formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde0356e2-3c92-47bd-8140-7f09e1bdd3c1%2F2e200b9c-9327-4fa7-a652-dd09d604a114%2F92bbewi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title:** Understanding the Slope of a Line
**Introduction:**
In this section, we will explore how to find the slope of a line using a graph.
**Graph Description:**
The graph provided displays a straight line plotted on a coordinate grid. The line slopes downward from the left to the right, crossing both the vertical (y-axis) and horizontal (x-axis) axes.
**Identifying Slope:**
1. **Identify Two Points:**
- The line intersects grid lines at two visible points. These points can be used to calculate the line's slope.
2. **Calculate Slope (m):**
- The slope \( m \) is determined by the formula:
\[
m = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}}
\]
- **Rise:** The change in the vertical direction (y-axis).
- **Run:** The change in the horizontal direction (x-axis).
3. **Example Calculation:**
- Find the vertical change (rise) between two points.
- Find the horizontal change (run) between the same points.
- Insert the values into the slope formula to find \( m \).
**Conclusion:**
The graph aids in visualizing how the slope represents the steepness and direction of a line. Calculating the slope is crucial in understanding linear relationships in algebra.
**Problem:**
Calculate the slope \( m \) for the given line using the graph.
---
Use this guide to understand how to determine the slope of any given line on a graph by visually identifying points and using the slope formula.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education