# Lrchiiisii - Chapter 3 Lines Parabolas and Systems 3.2...

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Chapter 3: Lines, Parabolas and Systems 3.2: APPLICATIONS AND LINEAR FUNCTIONS DR. RAJA LATIF September 17, 2005 Abstract

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We develop the notion of demand and supply curves and introduce lin- ear functions. SUPPLY AND DEMAND: The curves that show the quantity that will be supplied at a given price and the quantity that will be demanded at a given price are called SUPPLY and DEMAND CURVES. Supply and demand are equal at the point where the supply curve intersects the demand curve. This is the equilibrium point. Its second coordinate is the equilib- rium price, the price at which the same quantity will be supplied as is demanded. Its f rst coordinate is the quan- tity that will be demanded and supplied at the equilibrium price; this number is called either the equilibrium demand or the equilibrium supply.
Customarily, a demand equation (as well as a supply equation) expresses p in terms of q and actually de f nes a function of q . LINEAR FUNCTION: A function is a linear function if and only if f ( x ) can be written in the form f ( x )= ax + b, where a and b are constants and a 6 =0 . The graph of a linear function is a straight line. We say that the function f ( x )= ax + b has slope a.

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140AL4Example. (Demand) A dealer can sell 20 elec- tric shavers per day at \$25 per shaver, but he can sell 30 shavers if he charges \$20 per shaver. Determine the demand equation, assuming it is linear. Solution. Taking the quantity x demanded as the ab- scissa (or x coordinate) and the price p per unit as theo rd ina te(o r y coordinate), the two points on the demand curve have coordinates
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Lrchiiisii - Chapter 3 Lines Parabolas and Systems 3.2...

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