Math Problem Statement
Solution
The question shown in the image provides information about the demand for pies as a function of price. Let's break it down and solve it step by step.
(a) Determine the demand (number of pies sold) as a function of the price (in dollars).
The problem gives two points:
- When the price , the demand pies.
- When the price , the demand pies.
We can use the formula for a line , where is the slope and is the intercept.
To find the slope , use the formula for slope between two points and :
So, the slope is .
Now, substitute and use one of the points to solve for . Let's use and :
Therefore, the demand function is:
(b) What is the slope of the graph of ?
From the previous calculation, the slope of the graph is:
The slope represents the rate of change in the number of pies sold for each dollar increase in price. Specifically, for each 1-dollar increase in price, 9 fewer pies are sold.
If you have any questions or need more details, feel free to ask!
Related Questions:
- How would the graph of look like in terms of its intercepts?
- What happens to the demand when the price reaches $0?
- How would the demand change if the price increased by $2?
- What is the significance of the y-intercept in this context?
- How does elasticity relate to this linear demand function?
Tip:
Whenever dealing with a linear equation, the slope will always give you important insights into how one variable changes in response to another. In economics, it’s often used to understand demand or supply sensitivity.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Demand Functions
Formulas
N(P) = mP + b (Linear Equation for Demand)
m = (N2 - N1) / (P2 - P1) (Slope Calculation)
Theorems
Slope-Intercept Form
Linear Demand Models
Suitable Grade Level
Grades 9-11