Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![**Consider the following graph:**
The graph displays a linear relationship between "Disposable Income" (x-axis) and "Consumption" (y-axis). Two key points on the line are marked:
- Point A at (10,000, 4,000): When disposable income is 10,000, consumption is 4,000.
- Point B at (20,000, 8,000): When disposable income is 20,000, consumption is 8,000.
The graph also shows horizontal and vertical lines for reference, intersecting the key points on the axes.
**Question: The slope is:**
- ○ 1.2
- ○ indeterminate from this information
- ○ 2.5
- ○ 0.4
**Explanation of Calculation:**
The slope of a line is calculated as the change in the y-value (vertical change) divided by the change in the x-value (horizontal change).
Mathematically, the slope (m) is given by:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
For the given points A (10,000, 4,000) and B (20,000, 8,000):
\[ \Delta y = 8,000 - 4,000 = 4,000 \]
\[ \Delta x = 20,000 - 10,000 = 10,000 \]
So, the slope \( m \) is:
\[ m = \frac{4,000}{10,000} = 0.4 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0062e4a6-9690-49aa-88d1-44e3a48d2adc%2Fd76caab3-263a-4c30-b675-53bad79e0b93%2F243eeo_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following graph:**
The graph displays a linear relationship between "Disposable Income" (x-axis) and "Consumption" (y-axis). Two key points on the line are marked:
- Point A at (10,000, 4,000): When disposable income is 10,000, consumption is 4,000.
- Point B at (20,000, 8,000): When disposable income is 20,000, consumption is 8,000.
The graph also shows horizontal and vertical lines for reference, intersecting the key points on the axes.
**Question: The slope is:**
- ○ 1.2
- ○ indeterminate from this information
- ○ 2.5
- ○ 0.4
**Explanation of Calculation:**
The slope of a line is calculated as the change in the y-value (vertical change) divided by the change in the x-value (horizontal change).
Mathematically, the slope (m) is given by:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
For the given points A (10,000, 4,000) and B (20,000, 8,000):
\[ \Delta y = 8,000 - 4,000 = 4,000 \]
\[ \Delta x = 20,000 - 10,000 = 10,000 \]
So, the slope \( m \) is:
\[ m = \frac{4,000}{10,000} = 0.4 \]
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