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A farmer observes that the demand for corn, Q, in thousands of bushels per month, and price, P. in dollars per bushel, are related by a linear function. If a demand of 2,500 bushels per month corresponds to a price of $4.00 per bushel , and a demand of 3,000 bushels per month corresponds to a price of $3.20 per bushel, which of the following graphs represents the relationship between P and Q?​

User Karen B
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The relationship between demand and price is represented by a linear function. Using the given points, we can find the equation for this relationship by finding the slope and y-intercept. The correct graph representing this relationship is the one where the demand curve intersects the supply curve at a price of $2 and a quantity of 12.

Demand and Price Relationship in Linear Function

The relationship between demand, Q, and price, P, is represented by a linear function. We can find the equation for this relationship using the given information. From the data, we have two points: (2500, 4) and (3000, 3.20). Using these points, we can find the slope and y-intercept of the linear function. The equation will be in the form P = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m):

m = (P2 - P1) / (Q2 - Q1) = (3.20 - 4) / (3000 - 2500) = -0.8 / 500 = -0.0016

Next, let's find the y-intercept (b) using one of the points:

4 = -0.0016(2500) + b

b = 4 + 4 = 8

Therefore, the equation for the relationship between demand and price is:

P = -0.0016Q + 8

The graph of this equation will be a straight line with a negative slope (-0.0016) and a y-intercept at 8. The correct graph representing this relationship is the one where the demand curve (Qd) intersects the supply curve (Qs) at a price of $2 and a quantity of 12.

User Pawlik
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