In my Math book I'm solving a case where this is the situation:
"The demand curve for good X is linear. At a price (p) of 300 the demand is 600 units. At a price of 680 the demand is 220 units. Also the supply curve for good X is linear. If the price is 400 then the supply equals 200 units, whereas for a price of 800 the supply will be 1000 units."
I'm asked to formulate the system of equations.
For the demand function I did:
SLOPEqd = delta y / delta x = -1 (delta y 680-300, delta x 220-600)
Which I could use and verify by the coordinates and I got the formula Demand(x) = -x + 900)
If I do the same for the supply function I end up wrong:
SLOPEqs = delta y / delta x = 0.5 (delta y 800-400, delta x 1000-200)
If I try to verify this for the first supply point (800, 1000) I would get:
Supply(x) = 0,5x + 600 but this is incorrect for the second point (400, 200). In the answers I found the slope for the supply function should be 2 instead of 0,5. Why is this? I think I'm overlooking something super obvious, but please enlighten me.
(sorry, I haven't figured out how to write the equations as fancy as I see them in other questions)
Answer
You have your $x$ and $y$ co-ordinates the wrong way round. Supply is your $y$ co-ordinate (dependent variable) and Price is you $x$ co-ordinate (independent variable) so you should have
$\Delta y = 1000 - 200 = 800$
$\Delta x = 800 - 400 = 400$
$\text{Slope } = \frac{\Delta y}{\Delta x} = \frac{800}{400} = 2$
$\text{Supply } = 2 \times \text{Price } - 600$
You had your $x$ and $y$ co-ordinates the wrong way round in your Demand calculation as well, but since the slope there is $-1$ whichever way round you have the co-ordinates, this did not matter.
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