Math 141-copyright Joe Kahlig, 10A Page 1Section 1.2: LinesPoints: (3, 4), (7, 16)Slope:y2− y1x2− x1Equation of a line:Example: Determin if these lines intersect. If they do, find the point/points of intersection.A) x + y = 53x − 2y = 10B) x + 2y = 02x + 4y = 1Section 1.3 and 1.4: Linear Functions and ModelingExample: The percent of people with an iPad was at 6% at the beginning of 2010 and is projected togrow linearly s o that at the beginning of 2014 the percent of people with an iPad is projected to be 26%.A) Derive an equation of the line that represents this information.B) In what year will the percentage of homes with digital TV service be 49%?Math 141-copyright Joe Kahlig, 10A Page 2Example: The Monde Company makes a wine cooler with a capacity of 24 bottles. Each wine coolersells for $245. The monthly fixed cost incurred by th e company are $381,300, and the variable cost ofproducing each wine cooler is $90.A) Find the Cost, Revenue, and Profit functions.B) How many co olers should be made and sold when the company breaks even?C) What is the br eak even point?Example: Paul manages a t-shirt store which has a m onthly rent of $805. If Paul needs to sell 46shirts each month to break even and he sells the shirts for $28.50, what does Paul pay for each shirt?Supply and Demand functions:The supply function is a formula that relates the number of items being supplied by manufacturers,x, to the price of the items, p.The demand function is a formula that relates the number of items being demanded by consumers,x, to the price of the items, p.Note: All points for supply and demand formulas are given as (x, p).Market equilibrium is the point where the supply and demand functions intersect.Example: When a coffee m aker is priced at $40, 200 sell. If the price increases by $10, then 150 sell.The producer is willing to provide 240 coffee makers when the price is $160 and are willing to provide120 coffee makers when the price is $88. Find the supply and demand equations and then find theequilibrium
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