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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![**Graph Analysis and Equation Writing**
**Task:**
Write an equation to represent the graph below. The points are (0, -5) and (-1, -3).
**Graph Description:**
- The graph is a standard coordinate plane with x and y axes.
- A straight line passes through the points (0, -5) and (-1, -3).
**Steps to Write the Equation:**
1. Identify the points given: \( (0, -5) \) and \( (-1, -3) \).
2. Use the points to calculate the slope (\( m \)) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points:
\[
m = \frac{-3 - (-5)}{-1 - 0} = \frac{-3 + 5}{-1} = \frac{2}{-1} = -2
\]
3. Use the slope-intercept form of a line (\( y = mx + b \)), where \( b \) is the y-intercept.
4. Substitute the slope (\( m = -2 \)) and one of the points, say \( (0, -5) \), into the equation:
\[
-5 = -2(0) + b \quad \Rightarrow \quad b = -5
\]
5. Write the equation of the line:
\[
y = -2x - 5
\]
**Conclusion:**
The equation that represents the graph is \( y = -2x - 5 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4c8e957-9b5c-44fb-9b14-6fbe4755d261%2Fdc0810c8-c84d-4750-9530-c8e79a4ccf6f%2Fc10j8rj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph Analysis and Equation Writing**
**Task:**
Write an equation to represent the graph below. The points are (0, -5) and (-1, -3).
**Graph Description:**
- The graph is a standard coordinate plane with x and y axes.
- A straight line passes through the points (0, -5) and (-1, -3).
**Steps to Write the Equation:**
1. Identify the points given: \( (0, -5) \) and \( (-1, -3) \).
2. Use the points to calculate the slope (\( m \)) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points:
\[
m = \frac{-3 - (-5)}{-1 - 0} = \frac{-3 + 5}{-1} = \frac{2}{-1} = -2
\]
3. Use the slope-intercept form of a line (\( y = mx + b \)), where \( b \) is the y-intercept.
4. Substitute the slope (\( m = -2 \)) and one of the points, say \( (0, -5) \), into the equation:
\[
-5 = -2(0) + b \quad \Rightarrow \quad b = -5
\]
5. Write the equation of the line:
\[
y = -2x - 5
\]
**Conclusion:**
The equation that represents the graph is \( y = -2x - 5 \).
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