The price p in dollars and the quantity q sold of a product

The price p, in dollars, and the quantity q sold of a product are represented by a linear function. If the price of the product is $20, then 100 of these products are sold and if the price of the product is increased by $1 to $21, then 20 less of the product or 80 are sold. a) What is the slope of this linear function b) Write a formula to express q as a linear function of p. Show your work.

Solution

a)

Find the slope of line through point (20, 100) and (21, 80) as

slope = (80 -100)/(21-20)

= -20

Thus, slope is -20.

b)

Use the point slope forl to write equation of line as

q-100 = -20 (p -20)

q -100 = -20p +400

q= -20p +500