LINEAR MÔ HÌNH

CHAPTER 2

LINEAR FUNCTIONS AND MODELS
Temperature Reading
Scatter Plot Of The Data
Average Rate Of Change
The Average Rate of Change is Constant
Scatter Plot Of The Data
From the observations made in the previous slides we conclude that:
For instance if the temperature reading is 37 ºC then the corresponding temperature reading in degree Fahrenheit will be:
Population of Hypothetical City
Scatter Plot Of The Data
Average Rate of Change of Population
Average Rate of Change of Population
From the previous slide we observe that the population grows 6 thousands per year.
For instance in 2015 the population of the city will be:
Therefore
where t is the number of years since 1990.
Linear Functions
A function of the form
where a and b are real numbers, is called a linear function of x.
Sometimes we use y instead of f (x).
Straight Lines & Their Equations
A line in the rectangular coordinate plane can be represented algebraically by an equation of the form
An equation of this kind is called a linear equation in the variables x and y.
The graph of a linear equation is always a straight line.
If B ≠ 0 a linear equation can be written in slope-intercept form
Graphs Of Linear Equations
Vertical line
x = Constant
Horizontal Line
y = Constant
Intercepts of a Graph
To find x intercepts, let y be zero and solve the resulting equation for x.
To find y intercepts, let x be zero and solve the resulting equation for y.
How do we find intercepts?
Find the x- and y- intercepts of the linear equation
Graphing Linear Equations Using Intercepts
Suppose that P = (x1, y1) and Q = (x2, y2) are two points on a non vertical line as shown below.
Q = ( x2 , y2)
y
x
x2
y2
y1
x1
P = ( x1 , y1)
Slope Of Straight Lines
Vertical line
slope = Undefined
Horizontal Line
Slope = 0
Point-Slope Form Of A Linear Function
Two non-vertical lines are parallel if and only if they have the same slope.
Perpendicular lines
Piecewise-Linear Functions
Schedule X of the 2005 Form 1040 instructions specifies the tax paid by a single taxpayer as shown below:
2006 Tax Rate Schedules