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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Question
![### Find an Equation for the Line Below
The provided graph shows a straight line passing through the Cartesian plane. The x-axis (horizontal axis) and y-axis (vertical axis) are marked, with specific points plotted on the line.
#### Graph Details:
- The line has a negative slope, indicating it is decreasing when moving from left to right.
- Two points on the line are clearly visible:
- The first point is \((-3, 6)\).
- The second point is \((2, -4)\).
#### Steps to Find the Equation of the Line:
1. **Find the Slope (\(m\)):**
The slope of a line \(m\) can be found using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the coordinates from the points \((-3, 6)\) and \((2, -4)\):
\[
m = \frac{-4 - 6}{2 - (-3)} = \frac{-10}{5} = -2
\]
2. **Use Point-Slope Form:**
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-3, 6)\) and the slope \(-2\):
\[
y - 6 = -2(x + 3)
\]
3. **Simplify to Slope-Intercept Form (\(y = mx + b\)):**
Expand the equation:
\[
y - 6 = -2x - 6
\]
Solving for \(y\):
\[
y = -2x - 6 + 6
\]
This simplifies further to:
\[
y = -2x - 4
\]
Therefore, the equation of the line is:
\[
y = -2x - 4
\]
This equation represents the line shown in the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57f2dd19-0fae-4367-a918-e5b3d0fe23e2%2F02fb6533-fc42-4707-a6a8-b1d22c9ef844%2F44qymp9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Find an Equation for the Line Below
The provided graph shows a straight line passing through the Cartesian plane. The x-axis (horizontal axis) and y-axis (vertical axis) are marked, with specific points plotted on the line.
#### Graph Details:
- The line has a negative slope, indicating it is decreasing when moving from left to right.
- Two points on the line are clearly visible:
- The first point is \((-3, 6)\).
- The second point is \((2, -4)\).
#### Steps to Find the Equation of the Line:
1. **Find the Slope (\(m\)):**
The slope of a line \(m\) can be found using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the coordinates from the points \((-3, 6)\) and \((2, -4)\):
\[
m = \frac{-4 - 6}{2 - (-3)} = \frac{-10}{5} = -2
\]
2. **Use Point-Slope Form:**
The point-slope form of the equation of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-3, 6)\) and the slope \(-2\):
\[
y - 6 = -2(x + 3)
\]
3. **Simplify to Slope-Intercept Form (\(y = mx + b\)):**
Expand the equation:
\[
y - 6 = -2x - 6
\]
Solving for \(y\):
\[
y = -2x - 6 + 6
\]
This simplifies further to:
\[
y = -2x - 4
\]
Therefore, the equation of the line is:
\[
y = -2x - 4
\]
This equation represents the line shown in the graph.
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