algebra precalculus - Slope calculation misunderstanding for linear function

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.