Math-160-002
Yu Daiqing
April 20th 2015
Blog 4: Be the Professor
Topic of the lecture: Linear Function
Date: April 20th 2015
·
Introduction
Hello, everyone!
My name is Yu Daiqing, and you can call me Professor Yu or Miss Yu. Today I am
going to teach you about the Linear Function.
·
What is Liner Function?
Before we
begin our lecture of the linear function, I am sure that you all familiar with
the concept of rate of change. There are many other functions which has
different rate of change on different intervals. But, linear function has the
same rate of change on each intervals.
v
A
linear function has a constant rate of change.
v
The
graph of any linear function is a straight line.
Examples:
A town of 3000 people grows by 2000 people every year
(questions retrieved from book, page 19). 2000 people per year, then 5 years
later will be 10000 people.
v
Based
on all the information, you can put the numbers into a table as below.
v
Then
we use the table to create a linear function graph, see the second picture. As
we talked about before, a linear function looks exactly a straight line and the
rate of change in every interval is a constant numbers.
|
t
|
p
|
|
0
|
30000
|
|
5
|
40000
|
|
10
|
50000
|
|
15
|
60000
|
|
20
|
70000
|
·
General Formula of linear
function
If y=f (x) is a linear function, then for some constants b
and m:
y=b+mx
o
m
is called the slope, and gives the rate of change of y with respect to x. Thus,
m=△y/△x
If (x0 , y0 ) and
(x1 , y1) are any two distinct points on the graph of f,
then,
m=△y/△x= (y1- y0)/(x1-x0)
o
b
is called the vertical intercept, or y-intercept, and gives the value of y for
x=0. In mathematical models, b typically represents an initial, or starting,
value of the output.
(The definition above was retrieved from
book, page 21)
·
Real world examples
1. If you want to buy candy for the New
Year Party and you've got $40 in your pocket, a linear equation tells you how
much you can afford.
2.If you need to drive to Virginia by
car, then you need to calculate how much money you need pay for driving to
Virginia.
3. My T-Mobile cell phone plan might be $50 per month plus 25 cents per text
message. So the monthly bill would be?
· Conclusion
Linear functions are literally,
everywhere. The linear function is the most fundamental function when compared
with others. It can solve many basic problem which people face every day, for
example, weekly paycheck problems, gas problem, phone bill problems. In
addition, it is popular in economics, because it is simple and easy to understand.
Based on many real life situations, it is clear that Linear Function is really
important in math learning, since this function related to our life. So, have a
good understanding can help us solve daily problems. There is no doubt that this is a pragmatic math
concept.
Your post was easy to follow, and with the incorporation of a table and a graph, the concept came to life. It felt like a natrual extension of this class, and that is always a positive!
ReplyDeletei liked how you explained rate of change before going into linear functions! great job
ReplyDeletefish,
ReplyDeletei like your lesson. it is done well. your graphics are great and your table and graph look good. the only thing that would have been nice to see is the calculation of the slope since that coincides with the definition for a linear function and its graph being a straight line.
all in all, good job.
professor little