Emma's blog 4

Blog 4: Be a professor: What is linear function?

Lecture topic: Linear function

Date: April 19th 2015

Introduction:

Hello everyone, my name is Emma and I'm your new math professor for this semester. Today, I'm so happy to see you all and I'm going to teach you what is linear function and how to find linear function. 

What is Linear function?

We consider functions that have the same average rate of change on every interval. Such a function has a graph that is a line and is called linear. A linear function has a constant rate of change.

• Linear function is a simple and easy mathematical equation, which graph is a straight line. 
• The basic form of linear function is y = b + mx
• A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
• b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.
• m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.

Example one: 

y = 25 + x

let x = 1

then 

y = 25 + 5(1) = 30

let x = 3

then 

y = 25 + 5(3) = 40

 

• Rate of change of linear function= Change in output/ Change in input = Constant. 

Example two:

Tony had 5 gallons of gasoline in his motorbike. After driving 100 miles, he had 3 gallons left.

Question: Find the slope of the line?

Solution: Slope= Vertical change/ Horizontal change = -2/100 = -50. 

Question: What does the slope tell us? 

Solution: The rate of change tells us Tony can drives 50 miles on one gallon of gasoline. 

Conclusion:

We can use rate of change formula to find the function is a linear function or not. Linear function must be a straight line and the rate of change is always constant. In linear function, one input is always pair with one output. Thank you so much. 

Tddd