I'm having trouble with figuring out the steps for this problem

Question

The market equilibrium point for a product is reached when 10000 units are produced and sold at $30 per unit. The manufacturer will not produce any units at the price of $3, and the customers will not buy any at the price of $61.

Find the supply and demand equations, assuming they are linear. The equations should express price 𝑝p in terms of quantity 𝑞q.

Supply equation: 𝑝=p= 

Demand equation: 𝑝=p= 

Answer 1

(10, 30) = (q, p) = equilibrium with q measured in thousand units, p= $30, q=Qs = Qd = Quantity supplied = Quantity demanded. p= price is measured on the vertical or y axis. q=quantity is measured on the horizontal or x axis

(0, 61) = (Qd, p) Quantity demanded = 0 when p=$61

two points on the linear demand curve or (0,61) and (10,30). they have a line through them with slope = change in p divided by change in q = (61-30)/(0-10) =31/-10. the line's equation is p-30= (-31/10)(q-10) or p = -31q/10 + 61

the demand curve is p =-3.1q + 61

the Quantity supplied = 0 when p = $3, points on the supply curve are (0,3) and (10,30)

the slope of the supply line is (30-3)/(10-0) = 27/10

the supply line is p -3 = 2.7q or p = 2.7q +3

the supply line or supply curve is p=2.7q +3

demand curve: p=-3.1q +61 or p =-31q/10 + 61

supply curve: p =2.7q +3 or 27q/10 + 3

equilibrium is when -3.1q +61 = 2.7q +3

2.7q +3.1q = 61-3

5.8q = 58

q = 58/5.8 = 10 = 10,000 units bought and sold

p = 2.7q +3 = 27+3 = 30 = $30 = price when Qd = Qs

p = -3.1q +61 =-31+61 = $30 = price when Qd = Qs, when Quantity demanded = Quanty supplied

or use the point (10,000, 30) and do the same calculations