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 Dependent Variable

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# Linear Equations

• Price-Demand
• Price-Supply
• Simple Interest
• Linear equation practice problems

Price versus quantity demanded:
Several companies make a 37 inch, Plasma HDTV. Right now,
they sell for an average of \$1440. But what if the price goes
up? Then consumer demand will decrease. But if the price goes
down, then consumer demand will increase. Consumer demand
depends on the price.

Symbols:

• Price: p is the selling price for the TV.
• Demand: d is the number of TVs (in thousands) sold.

The quantity d of TVs sold (demanded) is related to the price p
as follows:
d = 1720 − .50p

Can you see how the equation below reflects the relationship?

Price-demand equation: d = 1720 − .50p
We are interested in pairs of number d and p (written (d, p))
that satisfy this equation. Such a pair is called a solution to the
equation.

What is the demand (in thousands) if the price is \$1440?
What is the demand if the price is \$2500?
What price should we charge if we want to sell 500 thousand
TVs?

Price-demand equation: d = 1720 − .50p

The demand (in thousands) if the price is \$1440 is
d = 1720 − (.50)(1440) = 1000 thousand TVs (one million)

What is the demand if the price is \$1441?

The demand (in thousands) if the price is \$2500 is
d = 1720 − (.50)(2500) = 470 thousand TVs

What is the demand if the price is \$2501?
If price increases \$1 how does demand change?

Price-demand equation: d = 1720 − .50p. Represent all such
solutions on a graph. Why is it straight? What point above represents the situation where the price is
\$1440?
What point above represents the situation where the price is
\$2500?
What point above represents the situation where the demand is
500 thousand TVs?

Price-demand equation: d = 1720 − .50p.

What are some other ways to write this equation?
What would it tell us if we solved for p in terms of d?

The equation d = 1720−.50p is and example of a linear equation
in two variables.

Price-supply:
The companies that make the 37 inch HDTVs are willing to
produce more TVs if they can sell them at a higher price. So
the supply of TVs is also related to the price at which these TVs
will sell.

The supply equation in this case is:
s = .375p+460
Again, supply is measured in thousands of TVs. This is also a
linear equation in two variables.

How does this equation match the description above?

Price-supply equation: s = .375p+460. Again we can represent
many solutions at once with a graph. Moreover we can use the What is the supply (in thousands) if the price is \$600?
What is the supply if the price is \$2500?

At what price does the quantity demanded match the quantity
supplied?

Price-demand function: d = 1720 − .50p
Price-supply function: s = .375p+460 Solve d = s. What does this have to do with the price p? Did you
have a linear equation? In how many variables? Clicker question

Simple Interest Formula:
Consider the following Symbols

• Principal P
• Interest rate (annual) r
• Time t
• Amount of money at end of investment period.

These are also related by a linear equation: A = P +Prt.

Solve for r. What does this mean?
Solve for t. What does this mean?

More Practice:
[Matched problem 8 Section1.1] Mary paid 8.5% sales tax and a
\$190 title and license fee when she bought a new car for a total
of \$28,400. What is the purchase price of the car?

More Practice:
[Matched problem 9 Section1.1] How many CDs would a recording
company have to make and sell to break even if the fixed
costs are \$18,000, variable costs are \$5.20 per CD and the CDs
are sold to retailers for \$7.60 each?