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
![**Graphing Linear Equations**
**Write an equation for the line graphed below**
[Insert Image with Line Graph]
The diagram shows a coordinate plane with both x and y-axes labeled from -6 to 6. A blue line is graphed, extending diagonally from the bottom-left quadrant to the top-right quadrant. The line crosses the y-axis at approximately y = -2 and the x-axis at approximately x = 2. The slope of the line is positive, indicating an upward trend as it moves from left to right.
To find the equation of the line, you can use the slope-intercept form of a linear equation: \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.
1. **Identify the y-intercept (b):**
The y-intercept (\( b \)) is the point where the line crosses the y-axis. From the graph, you can see that the line crosses the y-axis at \( y = -2 \). Thus, \( b = -2 \).
2. **Calculate the slope (m):**
The slope (\( m \)) is determined by the rise over run between two points on the line. From the graph, choose the points (-2, -3) and (1, 1).
\[
\text{Slope} (m) = \frac{\text{rise}}{\text{run}} = \frac{1 - (-3)}{1 - (-2)} = \frac{1 + 3}{1 + 2} = \frac{4}{3}
\]
3. **Write the equation:**
Substitute the slope (\( m \)) and y-intercept (\( b \)) into the slope-intercept form:
\[
y = \frac{4}{3}x - 2
\]
Therefore, the equation for the line graphed is \( y = \frac{4}{3}x - 2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22396abd-1dcc-4b0d-9124-fd12e74a7cb7%2F3ee9749f-850f-4fad-9be4-120c46b0bdb0%2F4mpo5i9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphing Linear Equations**
**Write an equation for the line graphed below**
[Insert Image with Line Graph]
The diagram shows a coordinate plane with both x and y-axes labeled from -6 to 6. A blue line is graphed, extending diagonally from the bottom-left quadrant to the top-right quadrant. The line crosses the y-axis at approximately y = -2 and the x-axis at approximately x = 2. The slope of the line is positive, indicating an upward trend as it moves from left to right.
To find the equation of the line, you can use the slope-intercept form of a linear equation: \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.
1. **Identify the y-intercept (b):**
The y-intercept (\( b \)) is the point where the line crosses the y-axis. From the graph, you can see that the line crosses the y-axis at \( y = -2 \). Thus, \( b = -2 \).
2. **Calculate the slope (m):**
The slope (\( m \)) is determined by the rise over run between two points on the line. From the graph, choose the points (-2, -3) and (1, 1).
\[
\text{Slope} (m) = \frac{\text{rise}}{\text{run}} = \frac{1 - (-3)}{1 - (-2)} = \frac{1 + 3}{1 + 2} = \frac{4}{3}
\]
3. **Write the equation:**
Substitute the slope (\( m \)) and y-intercept (\( b \)) into the slope-intercept form:
\[
y = \frac{4}{3}x - 2
\]
Therefore, the equation for the line graphed is \( y = \frac{4}{3}x - 2 \).
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