1.6 APPLICATIONS OF LINEAR
FUNCTIONS
QUIZ

Fill in the blank below:
A number y varies directly with x if there exists
a nonzero number k such that y=____
SOLVING APPLICATION PROBLEMS
Read the problem
Gather information, make a sketch, write what
the variable will represent.
 Write an equation
 Solve the equation
 Look back and check your solution
Verify that the answer makes sense, fullfills the
requirements.

EXAMPLE 1
The new generation of televisions has a 16:9
aspect ratio. This means that the length of the
television’s rectangular screen is 16/9 times its
width. If the perimeter of the screen is 136
inches, find the length and the width of the
screen.
EXAMPLE 2

In 1960 only 7% of physicians were female, but
the number had risen to 20% in 1992. Write a
linear function to describe the percentage of
physicians that are female in terms of the year.
Find the percentage of physicians that are female
in 2010.
BREAK-EVEN PROBLEM

For what number (x) of items sold will the
revenue collected equal the cost of producing
those items?
Revenue (R(x)) = selling price x # of items sold
Cost (C(x)) = fixed cost + item cost x # of items
sold
Break-even point: R(x) = C(x)
EXAMPLE

A student is planning to produce and sell music
DVDs for $5.50 each. A computer with a DVD
burner costs $2500, and each blank DVD costs
$1.50.
1. Find the revenue function R(x) and the cost
function C(x).
2. Find the break-even point.
3. Show the solution graphically. [What portion
of the graph shows the student is making a
profit?]
DIRECT VARIATION
When a situation gives rise to a linear function
f(x) = kx, or y = kx, we say that we have direct
variation
 The following three statements are equivalent.
1. y varies directly as x.
2. y is in direct proportion to x.
3. y = kx for some nonzero constant k.
The number k is the constant of variation.

EXAMPLE 1
If A varies directly as B, and B = 12 when A = 4,
find a linear model that relates A and B.
EXAMPLE 2
If w is proportional to t, and t = 18 when w = 10,
(a) find a linear model that relates w and t.
(b) use the model to find the value of w when t
= 639.
EXAMPLE 3

The cost of renting office space in a downtown
office building varies directly with the size of the
office. A 600-square-foot office rents for $2550 per
month. Use this information to write a model
that gives the rent in terms of the size of the
office. Then use the model to find the rent on a
960 square-foot office.
HOMEWORK

PG. 70: 31, 34, 35, 38, 41, 44, 53, 54, 55, 58, 60

KEY: 31, 34, 41, 60

Reading: 2.1 Basic Functions