MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Title: How to Determine the Equation of a Line from a Graph**
**Objective:**
Learn to write the equation of a straight line from a given graph using the slope-intercept form.
**Instructions:**
To write the equation of the line depicted in the graph, follow these steps:
1. **Identify Key Features:**
- **Slope (m):** The slope is the rise over the run. Choose two points on the line. For instance, on the graph, one point is (-8, 6) and another is (0, 3).
- Calculate the slope \( m \) as follows:
\[
m = \frac{{\text{change in } y}}{{\text{change in } x}} = \frac{3 - 6}{0 + 8} = \frac{-3}{8}
\]
2. **Y-Intercept (b):**
- The y-intercept is the point where the line crosses the y-axis. From the graph, this is point (0, 3), so \( b = 3 \).
3. **Equation of the Line:**
- Use the slope-intercept form of the line equation:
\[
y = mx + b
\]
- Substitute the slope and y-intercept into the equation:
\[
y = -\frac{3}{8}x + 3
\]
**Graph Description:**
The graph provided shows a straight line with a negative slope. It crosses the y-axis at y = 3 (y-intercept) and passes through the points (-8, 6) and (0, 3).
By following these steps, you can determine the equation of any straight line graph using the slope-intercept form.](https://content.bartleby.com/qna-images/question/1d3f2bfb-a5cc-4b06-99e2-b36f9d38db79/c4125839-16d8-4093-9eb6-812015a972de/q9ens9r_processed.jpeg)
Transcribed Image Text:**Title: How to Determine the Equation of a Line from a Graph**
**Objective:**
Learn to write the equation of a straight line from a given graph using the slope-intercept form.
**Instructions:**
To write the equation of the line depicted in the graph, follow these steps:
1. **Identify Key Features:**
- **Slope (m):** The slope is the rise over the run. Choose two points on the line. For instance, on the graph, one point is (-8, 6) and another is (0, 3).
- Calculate the slope \( m \) as follows:
\[
m = \frac{{\text{change in } y}}{{\text{change in } x}} = \frac{3 - 6}{0 + 8} = \frac{-3}{8}
\]
2. **Y-Intercept (b):**
- The y-intercept is the point where the line crosses the y-axis. From the graph, this is point (0, 3), so \( b = 3 \).
3. **Equation of the Line:**
- Use the slope-intercept form of the line equation:
\[
y = mx + b
\]
- Substitute the slope and y-intercept into the equation:
\[
y = -\frac{3}{8}x + 3
\]
**Graph Description:**
The graph provided shows a straight line with a negative slope. It crosses the y-axis at y = 3 (y-intercept) and passes through the points (-8, 6) and (0, 3).
By following these steps, you can determine the equation of any straight line graph using the slope-intercept form.
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