Write an equation of the line below. 8. 7. 6- 5. 3. 2- ロ=ロ -8 -7 -2 4. 6.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![## Mathematical Readiness
### Writing an Equation of a Line Given the y-Intercept and Another Point
**Task:**
Write an equation of the line below.
**Graph Explanation:**
The graph shows a line plotted on a standard Cartesian coordinate system. The x-axis and y-axis range from -8 to 8 in their respective directions. The line passes through the following notable points:
- A y-intercept at (0, 2)
- Another point at (1, 3)
The line moves upward from left to right, indicating a positive slope.
To find the equation of the line, you can use the slope-intercept form: \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
1. **Determine the Slope (\( m \)):**
The slope \( m \) is calculated as the change in y divided by the change in x between two points on the line.
\[
m = \frac{3 - 2}{1 - 0} = 1
\]
2. **Identify the y-Intercept (\( b \)):**
The line crosses the y-axis at (0, 2), so the y-intercept \( b \) is 2.
3. **Equation of the Line:**
Substituting the slope and y-intercept into the slope-intercept form gives:
\[
y = 1x + 2 \text{ or simplified, } y = x + 2
\]
This equation represents the line shown on the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d3f2bfb-a5cc-4b06-99e2-b36f9d38db79%2Ff0a438e6-b894-4ece-9832-f9f7287d18e7%2F9ay7gkp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Mathematical Readiness
### Writing an Equation of a Line Given the y-Intercept and Another Point
**Task:**
Write an equation of the line below.
**Graph Explanation:**
The graph shows a line plotted on a standard Cartesian coordinate system. The x-axis and y-axis range from -8 to 8 in their respective directions. The line passes through the following notable points:
- A y-intercept at (0, 2)
- Another point at (1, 3)
The line moves upward from left to right, indicating a positive slope.
To find the equation of the line, you can use the slope-intercept form: \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
1. **Determine the Slope (\( m \)):**
The slope \( m \) is calculated as the change in y divided by the change in x between two points on the line.
\[
m = \frac{3 - 2}{1 - 0} = 1
\]
2. **Identify the y-Intercept (\( b \)):**
The line crosses the y-axis at (0, 2), so the y-intercept \( b \) is 2.
3. **Equation of the Line:**
Substituting the slope and y-intercept into the slope-intercept form gives:
\[
y = 1x + 2 \text{ or simplified, } y = x + 2
\]
This equation represents the line shown on the graph.
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