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
![### Writing the Equation of a Line
To find the equation of the line passing through the points \((-1, 2)\) and \((6, 3)\), follow these steps:
1. **Calculate the slope (m)**:
The slope of a line that passes through two points, \((x_1, y_1)\) and \((x_2, y_2)\), is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points \((-1, 2)\) and \((6, 3)\):
\[
m = \frac{3 - 2}{6 + 1} = \frac{1}{7}
\]
2. **Use the point-slope form to find the equation**:
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-1, 2)\) and the slope \(m = \frac{1}{7}\):
\[
y - 2 = \frac{1}{7}(x + 1)
\]
3. **Simplify and convert to standard form**:
Expand and simplify the equation to convert it to standard form \(Ax + By = C\):
\[
y - 2 = \frac{1}{7}(x + 1)
\]
Multiply both sides by 7 to eliminate the fraction:
\[
7(y - 2) = x + 1
\]
Distribute and rearrange terms:
\[
7y - 14 = x + 1
\]
Combine like terms to get the standard form:
\[
-x + 7y = 15
\]
Or, multiplying through by -1 (to make \(x\) coefficient positive):
\[
x - 7y = -15
\]
Therefore, the equation of the line in standard form is:
\[
\boxed{x - 7y = -15}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1437a046-45d0-460d-9d0e-bc1ea076a72e%2F90554615-d911-4416-b1c7-c0f22e17c821%2Fzrarpq3_processed.png&w=3840&q=75)
Transcribed Image Text:### Writing the Equation of a Line
To find the equation of the line passing through the points \((-1, 2)\) and \((6, 3)\), follow these steps:
1. **Calculate the slope (m)**:
The slope of a line that passes through two points, \((x_1, y_1)\) and \((x_2, y_2)\), is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points \((-1, 2)\) and \((6, 3)\):
\[
m = \frac{3 - 2}{6 + 1} = \frac{1}{7}
\]
2. **Use the point-slope form to find the equation**:
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-1, 2)\) and the slope \(m = \frac{1}{7}\):
\[
y - 2 = \frac{1}{7}(x + 1)
\]
3. **Simplify and convert to standard form**:
Expand and simplify the equation to convert it to standard form \(Ax + By = C\):
\[
y - 2 = \frac{1}{7}(x + 1)
\]
Multiply both sides by 7 to eliminate the fraction:
\[
7(y - 2) = x + 1
\]
Distribute and rearrange terms:
\[
7y - 14 = x + 1
\]
Combine like terms to get the standard form:
\[
-x + 7y = 15
\]
Or, multiplying through by -1 (to make \(x\) coefficient positive):
\[
x - 7y = -15
\]
Therefore, the equation of the line in standard form is:
\[
\boxed{x - 7y = -15}
\]
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 9 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.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