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
Find an equation for the line with slope m= - 10/9 and which the point (-9, 8)
![**Question:**
Find an equation for the line with slope \( m = -\frac{10}{9} \) and which goes through the point \((-9, 8)\).
### Explanation:
To find the equation of the line, you can use the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
Where:
- \( m = -\frac{10}{9} \) is the slope
- \( (x_1, y_1) = (-9, 8) \) is the point the line passes through
**Steps:**
1. Substitute the slope and the point into the formula:
\[
y - 8 = -\frac{10}{9}(x + 9)
\]
2. Distribute the slope on the right side:
\[
y - 8 = -\frac{10}{9}x - 10
\]
3. Solve for \( y \) to find the equation in slope-intercept form:
\[
y = -\frac{10}{9}x - 10 + 8
\]
4. Simplify further:
\[
y = -\frac{10}{9}x - 2
\]
Thus, the equation of the line is:
\[
y = -\frac{10}{9}x - 2
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe84762dd-baf9-4e17-b4ea-3980bb4862e9%2F841b8d53-53b5-498c-9a91-dfaf77717456%2Fxxrzsx3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Find an equation for the line with slope \( m = -\frac{10}{9} \) and which goes through the point \((-9, 8)\).
### Explanation:
To find the equation of the line, you can use the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
Where:
- \( m = -\frac{10}{9} \) is the slope
- \( (x_1, y_1) = (-9, 8) \) is the point the line passes through
**Steps:**
1. Substitute the slope and the point into the formula:
\[
y - 8 = -\frac{10}{9}(x + 9)
\]
2. Distribute the slope on the right side:
\[
y - 8 = -\frac{10}{9}x - 10
\]
3. Solve for \( y \) to find the equation in slope-intercept form:
\[
y = -\frac{10}{9}x - 10 + 8
\]
4. Simplify further:
\[
y = -\frac{10}{9}x - 2
\]
Thus, the equation of the line is:
\[
y = -\frac{10}{9}x - 2
\]
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