Write an equation (a) in standard form and (b) in slope-intercept form for the line described. through (5,7), parallel to y = - 9 (a) The equation of the line in standard form is (Type your answer in standard form.)
Write an equation (a) in standard form and (b) in slope-intercept form for the line described. through (5,7), parallel to y = - 9 (a) The equation of the line in standard form is (Type your answer in standard form.)
Algebra and Trigonometry (6th Edition)
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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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solve for (a) and (b)
![### Problem Description:
Write an equation in two forms: standard form (a) and slope-intercept form (b) for the line described.
**Given:**
- The line passes through the point (5,7).
- The line is parallel to the line given by y = -9.
### Tasks:
1. **(a) The equation of the line in standard form:**
- Provide the equation in standard form.
- Input your answer in the provided text box in standard form.
2. **(b) Convert the same equation into slope-intercept form:**
- Provide the equation in slope-intercept form.
### Step-by-Step Solution:
#### 1. Understanding the problem:
- Since the line is parallel to y = -9, it has the same slope. This line is a horizontal line where y always equals -9, regardless of the value of x.
- Therefore, any line parallel to y = -9 will also be a horizontal line with the same slope (slope = 0) but passing through a different y-coordinate.
#### 2. Finding the equations:
- To find the equation of the line passing through the point (5, 7) and parallel to y = -9, we notice that it's a horizontal line where y = 7 for all x-values.
**(a) Standard Form:**
- For a horizontal line, the standard form is simply y = [constant].
- Here, y = 7. In standard form, this can be written as:
\[ \boxed{0x + 1y = 7} \]
**(b) Slope-Intercept Form:**
- The given form of the line y = 7 is already in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept). In this case, the slope (m) is 0, and the intercept (b) is 7.
\[ \boxed{y = 7} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15f5ca82-6bd2-4b6f-83d0-dbac308eccea%2Facf9fc45-bd29-47e5-a43a-b6cbd068abc8%2Foc0uc4m_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description:
Write an equation in two forms: standard form (a) and slope-intercept form (b) for the line described.
**Given:**
- The line passes through the point (5,7).
- The line is parallel to the line given by y = -9.
### Tasks:
1. **(a) The equation of the line in standard form:**
- Provide the equation in standard form.
- Input your answer in the provided text box in standard form.
2. **(b) Convert the same equation into slope-intercept form:**
- Provide the equation in slope-intercept form.
### Step-by-Step Solution:
#### 1. Understanding the problem:
- Since the line is parallel to y = -9, it has the same slope. This line is a horizontal line where y always equals -9, regardless of the value of x.
- Therefore, any line parallel to y = -9 will also be a horizontal line with the same slope (slope = 0) but passing through a different y-coordinate.
#### 2. Finding the equations:
- To find the equation of the line passing through the point (5, 7) and parallel to y = -9, we notice that it's a horizontal line where y = 7 for all x-values.
**(a) Standard Form:**
- For a horizontal line, the standard form is simply y = [constant].
- Here, y = 7. In standard form, this can be written as:
\[ \boxed{0x + 1y = 7} \]
**(b) Slope-Intercept Form:**
- The given form of the line y = 7 is already in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept). In this case, the slope (m) is 0, and the intercept (b) is 7.
\[ \boxed{y = 7} \]
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