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Question 1180957: A local dairy association enlists the help of a marketing research firm to predict the demand for milk. The research firm finds that the local demand for milk can be predicted the equation q=-4000p+10000, where p represents the price quarter and q represents the number of quarters purchased per week.
Graph the equation.
Identify the slope and q intercept.
Interpret the meaning of slope and q intercept in this application.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to analyze the milk demand equation:
**1. Graphing the Equation:**
The equation q = -4000p + 10000 is a linear equation, so its graph will be a straight line. To graph it, we can find two points and connect them. The easiest points to find are the intercepts:
* **q-intercept:** This is where p = 0. Substituting p = 0 into the equation gives q = -4000(0) + 10000 = 10000. So, the q-intercept is (0, 10000).
* **p-intercept:** This is where q = 0. Substituting q = 0 into the equation gives 0 = -4000p + 10000. Solving for p, we get 4000p = 10000, so p = 10000 / 4000 = 2.5. So, the p-intercept is (2.5, 0).
Plot these two points (0, 10000) and (2.5, 0) on a graph where the horizontal axis is 'p' (price) and the vertical axis is 'q' (quantity). Connect the points with a straight line. Since price and quantity are usually non-negative, you only need to show the first quadrant of the graph.
**2. Identifying the Slope and q-intercept:**
* **Slope:** The equation is in the form q = mp + b, where 'm' is the slope and 'b' is the q-intercept. In this case, the slope is -4000.
* **q-intercept:** As we already found, the q-intercept is 10000.
**3. Interpreting the Meaning of Slope and q-intercept:**
* **Slope (-4000):** The slope represents the change in the quantity of milk purchased (q) for every one-unit change in price (p). Specifically, a slope of -4000 means that for every $1 increase in the price per quarter, the quantity of milk purchased decreases by 4000 quarters per week. The negative sign indicates an inverse relationship between price and quantity demanded, which is typical for demand curves.
* **q-intercept (10000):** The q-intercept represents the quantity of milk purchased per week when the price is $0. In other words, if milk were free, the local dairy association could expect to sell 10,000 quarters per week. While this might seem unrealistic, it's a theoretical point on the demand curve. It helps define the curve and it's a useful point to understand the overall demand for milk.
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