Answer: Q = -60p+210
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Step-by-step explanation:
For now, I'll use x in place of p and y in place of Q
So,
- x = P = price in dollars
- y = Q = quantity demanded in gallons
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Let's pick apart the given info
- "At a price of $2.80 per gallon, the average weekly demand for gasoline by consumers is 42 gallons" boils down to "price = 2.80 so people want 42 gallons". So we have x = 2.80 pair up with y = 42.
- "If the price rises to $2.85, the average weekly demand drops to 39 gallons" means that x = 2.85 and y = 39 pair up
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We have the two points (2.80, 42) and (2.85, 39)
Let's find the slope of the line through those two points.
m = (y2-y1)/(x2-x1)
m = (39-42)/(2.85-2.80)
m = -3/0.05
m = -60
The slope is negative to indicate each time the price goes up, the amount demanded goes down. We have an inverse relationship going on here.
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Now turn to y = mx+b. We know m as found in the previous section above. We just need the value of b. Use either (x,y) pair to find b. I'll use the first ordered pair.
y = mx+b
y = -60x+b ... replace m with -60
42 = -60(2.80)+b ... plug in (x,y) = (2.80,42)
42 = -168+b
42+168 = b
210 = b
b = 210 is the y intercept
If the price were x = 0, then theoretically the amount demanded would be y = 210 gallons. This is assuming the linear trend holds up of course.
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With m = -60 and b = 210, we then go from y = mx+b to y = -60x+210
The last step is to replace x and y with p and Q respectively getting the final answer Q = -60p+210
As a check, we can plug in something like p = 2.80 and we should get Q = 42
Let's find out
Q = -60p+210
Q = -60(2.80)+210
Q = -168+210
Q = 42
So that confirms the first point (2.80, 42). I'll let you check the other point. You should get Q = 39 when you plug in p = 2.85