Math 141-copyright Joe Kahlig, 15A
Page 1
Section 1.2: Lines
Points: (3, 4), (7, 16)
Slope:
y2 − y1
x2 − x1
Equation of a line:
Section 1.3 and 1.4: Linear Functions and Modeling
Example: The percent of people with an iPad was at 6% at the beginning of 2010 and is projected to
grow linearly so 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 people with ipads be 49%?
Math 141-copyright Joe Kahlig, 15A
Page 2
Example: The Monde Company makes a wine cooler with a capacity of 24 bottles. Each wine cooler
sells for $245. The monthly fixed cost incurred by the company are $381,300, and the variable cost of
producing each wine cooler is $90.
A) Find the Cost, Revenue, and Profit functions.
B) How many coolers should be made and sold when the company breaks even?
C) What is the break even point?
Example: Paul manages a t-shirt store which has a monthly rent of $805. If Paul needs to sell 46
shirts each month to break even and he sells the shirts for $28.50, what does Paul pay for each shirt?
Math 141-copyright Joe Kahlig, 15A
Page 3
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 maker 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 provide
120 coffee makers when the price is $88. Find the supply and demand equations and then find the
equilibrium point.