Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Line Graph Analysis
#### Diagram Description:
This is a Cartesian coordinate system graph where the x-axis ranges from 0 to 5, and the y-axis ranges from 0 to 5. The grid is divided into unit squares, forming a 5x5 square.
#### Graph Explanation:
The graph displays a single diagonal line decreasing from the point (0, 4) on the y-axis to point (3, 0) on the x-axis. The line has a negative slope, indicating a downward trend.
#### Equation of the Line:
To find the equation of a straight line, use the formula: \( y = mx + c \).
- **Slope (m):**
The slope is calculated as the change in y divided by the change in x:
\[
m = \frac{0 - 4}{3 - 0} = \frac{-4}{3}
\]
- **Y-intercept (c):**
The line crosses the y-axis at (0, 4).
Thus, the equation of the line is:
\[ y = -\frac{4}{3}x + 4 \]
### Conclusion:
In the diagram, the equation for this line is \( y = -\frac{4}{3}x + 4 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65a8e990-5360-43af-b3a8-27c1c40fb79a%2F90255a40-a228-448f-be6a-c30e3d9bae6a%2F9i6fc74_processed.png&w=3840&q=75)
Transcribed Image Text:### Line Graph Analysis
#### Diagram Description:
This is a Cartesian coordinate system graph where the x-axis ranges from 0 to 5, and the y-axis ranges from 0 to 5. The grid is divided into unit squares, forming a 5x5 square.
#### Graph Explanation:
The graph displays a single diagonal line decreasing from the point (0, 4) on the y-axis to point (3, 0) on the x-axis. The line has a negative slope, indicating a downward trend.
#### Equation of the Line:
To find the equation of a straight line, use the formula: \( y = mx + c \).
- **Slope (m):**
The slope is calculated as the change in y divided by the change in x:
\[
m = \frac{0 - 4}{3 - 0} = \frac{-4}{3}
\]
- **Y-intercept (c):**
The line crosses the y-axis at (0, 4).
Thus, the equation of the line is:
\[ y = -\frac{4}{3}x + 4 \]
### Conclusion:
In the diagram, the equation for this line is \( y = -\frac{4}{3}x + 4 \).
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