how would I set up thie equation

Question

Suppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p).

Answer 1

p=mx+b. When x=42, p=$20 and when x=52, p=$10, so we have two points (42,20) and (52,10).

20=42m+b and 10=52m+b.

Subtract the second equation from the first: 10=-10m so m=-1.

20=-42+b, so b=62, therefore p=62-x or p=-x+62.