Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Plot the following system of equations on the following graph.
|
System of Equations:
|
|---|
| p=6−2qp=6−2q |
| p=4+qp=4+q |
Transcribed Image Text:The graph displays two linear equations plotted on a Cartesian plane with variables \(p\) and \(q\).
### Graph Explanation
- **Axes**:
- The horizontal axis (x-axis) is labeled as \(q\), ranging from 0 to 10.
- The vertical axis (y-axis) is labeled as \(p\), ranging from 0 to 10.
- **Lines**:
- A **blue line** represents the equation \(p = 4 + q\).
- It starts at the point (0,4) on the y-axis and moves upward to the right, intersecting the point (6,10). This line has a positive slope of 1.
- An **orange line** represents the equation \(p = 6 - 2q\).
- It starts at the point (0,6) on the y-axis and moves downward to the right, crossing the point (3,0). This line has a negative slope of -2.
- **Intersection**:
- The two lines intersect at the point \( (1, 5)\).
### Key Information
- **Equation 1**: \(p = 4 + q\)
- Slope: 1
- Y-intercept: 4
- **Equation 2**: \(p = 6 - 2q\)
- Slope: -2
- Y-intercept: 6
This visualization helps in understanding the concepts of linear equations and their graphical representations. The graph highlights the relationship between the variables \(p\) and \(q\) as expressed by the given equations.
Expert Solution
Step 1
Given
Demand equation p = 6-2q
Supply equation p = 4 + q
intercept of demand curve when P = 0 q = 3 units
when Q = 0, P = 6
Intercept of supply curve when Q = 0, p = 4
when q = 6, p = 10
Step by step
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