Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![**Problem Statement:**
"Write the equation of the line described.
Through (7, 3) and (-6, 2)."
**Instructions:**
Enter the equation of the line in the provided text box. Once completed, click the "Submit Answer" button.
**Solution Process:**
1. **Determine the Slope (m):**
Use the formula for slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
With the points (7, 3) and (-6, 2):
\[
m = \frac{2 - 3}{-6 - 7} = \frac{-1}{-13} = \frac{1}{13}
\]
2. **Write the Equation in Point-Slope Form:**
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using point (7, 3):
\[
y - 3 = \frac{1}{13}(x - 7)
\]
3. **Convert to Slope-Intercept Form (Optional):**
Solve for y to express the equation in slope-intercept form (\( y = mx + b \)):
\[
y - 3 = \frac{1}{13}x - \frac{7}{13}
\]
\[
y = \frac{1}{13}x + \frac{32}{13}
\]
**Submit Answer:**
Ensure your final answer is correctly filled in the box and press "Submit Answer" to check your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee05acd4-e32c-4a2d-aafd-cc4cda76f89e%2F1c4dcb52-413d-47dd-a24e-97bf2dbec8e7%2Fngtvyk.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
"Write the equation of the line described.
Through (7, 3) and (-6, 2)."
**Instructions:**
Enter the equation of the line in the provided text box. Once completed, click the "Submit Answer" button.
**Solution Process:**
1. **Determine the Slope (m):**
Use the formula for slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
With the points (7, 3) and (-6, 2):
\[
m = \frac{2 - 3}{-6 - 7} = \frac{-1}{-13} = \frac{1}{13}
\]
2. **Write the Equation in Point-Slope Form:**
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using point (7, 3):
\[
y - 3 = \frac{1}{13}(x - 7)
\]
3. **Convert to Slope-Intercept Form (Optional):**
Solve for y to express the equation in slope-intercept form (\( y = mx + b \)):
\[
y - 3 = \frac{1}{13}x - \frac{7}{13}
\]
\[
y = \frac{1}{13}x + \frac{32}{13}
\]
**Submit Answer:**
Ensure your final answer is correctly filled in the box and press "Submit Answer" to check your solution.
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