Give the slope and the y-intercept of the line with the given equation. Then, graph the linear equation. y = 8x + 2
Give the slope and the y-intercept of the line with the given equation. Then, graph the linear equation. y = 8x + 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Understanding the Slope and y-Intercept of a Linear Equation
**Objective:**
Determine the slope and y-intercept of a line with the given equation and graph the linear equation.
#### Given Equation:
\[ y = 8x + 2 \]
#### Steps to Identify the Slope and y-Intercept:
1. **Identify the Slope (m):**
In the equation \( y = mx + c \), the coefficient of \( x \) represents the slope. Here, the slope \( m \) is \( 8 \).
2. **Identify the y-Intercept (c):**
The constant term in the equation represents the y-intercept. Here, the y-intercept \( c \) is \( 2 \).
#### Graphing the Linear Equation:
- **Setup:**
A coordinate plane is provided, with the x-axis ranging from \(-2\) to \(6\) and the y-axis ranging from \(-2\) to \(8\).
- **Plotting Points and Drawing the Line:**
1. Begin at the y-intercept (0, 2) and place a point.
2. Use the slope \( 8 \) to find another point. Since the slope is \( \frac{\Delta y}{\Delta x} = \frac{8}{1} \), from the y-intercept move 1 unit to the right (positive direction on the x-axis) and 8 units up (positive direction on the y-axis). This gives another point at (1, 10).
3. Draw a line through these points to establish the graph of the equation \( y = 8x + 2 \).
#### Graph Description:
The graph confirms the equation by linearly connecting the points according to the slope and y-intercept. The line clearly shows a steep incline due to the high slope value, intercepting the y-axis at 2.
For an interactive, educational exploration of linear equations, students can adjust the slope and y-intercept values to observe how the graph changes accordingly. This visualization strengthens the understanding of the relationship between the equation of a line and its graph on a coordinate plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffeeb79a1-23ea-4f54-b610-a8910f30c066%2Fba477a29-c59e-492f-8607-bc3ebb404bc4%2Fcrlzub_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Slope and y-Intercept of a Linear Equation
**Objective:**
Determine the slope and y-intercept of a line with the given equation and graph the linear equation.
#### Given Equation:
\[ y = 8x + 2 \]
#### Steps to Identify the Slope and y-Intercept:
1. **Identify the Slope (m):**
In the equation \( y = mx + c \), the coefficient of \( x \) represents the slope. Here, the slope \( m \) is \( 8 \).
2. **Identify the y-Intercept (c):**
The constant term in the equation represents the y-intercept. Here, the y-intercept \( c \) is \( 2 \).
#### Graphing the Linear Equation:
- **Setup:**
A coordinate plane is provided, with the x-axis ranging from \(-2\) to \(6\) and the y-axis ranging from \(-2\) to \(8\).
- **Plotting Points and Drawing the Line:**
1. Begin at the y-intercept (0, 2) and place a point.
2. Use the slope \( 8 \) to find another point. Since the slope is \( \frac{\Delta y}{\Delta x} = \frac{8}{1} \), from the y-intercept move 1 unit to the right (positive direction on the x-axis) and 8 units up (positive direction on the y-axis). This gives another point at (1, 10).
3. Draw a line through these points to establish the graph of the equation \( y = 8x + 2 \).
#### Graph Description:
The graph confirms the equation by linearly connecting the points according to the slope and y-intercept. The line clearly shows a steep incline due to the high slope value, intercepting the y-axis at 2.
For an interactive, educational exploration of linear equations, students can adjust the slope and y-intercept values to observe how the graph changes accordingly. This visualization strengthens the understanding of the relationship between the equation of a line and its graph on a coordinate plane.
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