Situations involving Linear Functions?

Question

Can anyone give me situations/world problems involving linear functions and how to solve them?

Answer 1

one call company charges $55 per month, and $0.10 per call.
Another, $60 per month, and $0.08 per call.

what number of calls for charge to be equal?
When is plan A better; when B?

plan a: C=55+0.10x
plan b: C=60+0.08x
equate them
55+0.1x=60+0.08x
0.02x=5
x=5/.02
=250 calls

and plan a better for less than 250 calls; while b better for more than 250 calls.

Answer 2

A linear function would graph as a straight line and would follow the rule that for any value of x, there is one and only one value of y. For example:

f(x) = 3x + 1
y = x -12

World example:

Apples are 50¢ a doz. How much would 3 doz. cost?

Cost of Apples per doz., or x, = 0.5
No. of doz. = 3
Total Cost, or z, = xy
z= 0.5 x 3
z = 1.5, or $1.50

A non-linear function would graph as a curved line, or lines, and would have an exponential term in the expression. For example:

f(x) = 3x² + 2x -1
y = x²

These are a second order equations and x would have two values, or roots, one of which could be an imaginary number (√-1 is an imaginary number).

f(x) = x³
y = 2x³ + x² -x -9

These would be a third order equations and x would have 3 roots.

Answer 3

In busienss many times when figuring break even formula there is one linear equation for what it costs and one linear equation for profits and where they cross that is your break even point.