Linear Models
Year Population(millions)
2003 8.41
2004 8.52
2005 8.66
2006 8.85
2007 9.04
2008 9.22
Create a scatterplot of the population for North Carolina on your graphing calculator.
Linear Models
Define the variables
t = years since 2000
P = population of North Carolina in millions
Linear Models: TI –84
Input data: Go to STAT and 1:Edit Go to the top of L1 and clear Go to the top of L2 and clear
L1 represents x or horizontal axisL2 represents y or vertical axis
Go to L1 and enter the valuesGo to L2 and enter the values on the
table
Linear Models: TI –84
Domain/RangeSelect WINDOW and you will see:Xmin = smaller than smallest inputXmax= larger than largest inputXscal= Ymin= smaller than the smallest outputYmax= larger than largest outputYscal=Each will be based on the domain and range of
the values from the table.
Linear Models: TI –84Graphing Points
• Enter 2nd and y =• A screen with STAT PLOTS• Choose 1:1: Plot 1 enter• Make sure Plot 1 is on and the X list is
designated L1• Y list: L2• Also make sure Type: shows scatter plot.• Finally select Graph and the plot will show on
the screen.
Graphing Line on TI- 84
• Choose the two points that will make the line the best fit, and solve for the equation
• 8.41 – 9.04 3 - 7
m = 0.1575 (round to nearest hundredth)Y-intercept y = 0.16x + b 8.41 = 0.16(3) + b 8.41 = 0.48 + b 7.93 = b
Graphing Line on TI- 84
y = 0.16x + 7.93Select y = , buttonEnter the equation found 0.16x + 7.93Use the X,T,ϴ,n button to insert x into the
equation.Once the equation is entered select GRAPHA line will be drawn through the points that
were previously plotted.
Total Revenue for GE
a) Find an equation for a model of these data.
b) Using your model, estimate GE’s revenue in 2010
c)What is the slope of your model?
What does it mean in regard to GE’s revenue
Year Revenue
(Billions $)
2004 124
2005 136
2006 152
2007 172
2008 183
Relation
Relationship between elements of a set of input and elements of a set of outputs
(2,3)
x + 2y = 12
Relates x-values with y-values
using arithmetic operation
Function
For every input there is only one output
{(1,2) , (3,4) , (5, 6) , (7,8)}
123
567
Input Output x y
1 5
2 5
3 5
Function or Not?
• The set A = {(2,5) , (4,8) , (10,8) , (20, 15)}
• Weekly salaries during the mth month of the year.
Day of week Monday Wednesday Saturday Monday
Temperature
F
90 88 91 93
Notation
f(x)
“f of x” Represents a function named f that
depends on the variable xf means output/y-variable/range
Shorthand method of providing information in a compact form.
Word problems and Function Notation
a) H(t) = height of a toy rocket in feet t seconds after launch.
What does H(3) = 12 mean?
b) C(m) = Cost in hundred of dollars for producing m miracle mops.
C (2500) = 189
c) P(t) = population of Michigan, in millions, t, years since 2000.
P(10) = 10.4
Population of Wisconsin, in millions
• Find an equation for a model of these data. Write your model in function notation.
• Determine a reasonable domain and range
• Find P(14) and interpret its meaning in regard to the pop of Wisconsin.
Year Population
(millions)
2003 5.47
2004 5.51
2005 5.54
2006 5.57
2007 5.60
2008 5.63
Review
• f(x) = 4x + 3 f(3)
Domain and range is not restricted
Word problems Domain and range is set by the problem.
Systems of Equations
Set of equations that require a solution that will work for all of the equations in the set.
y= x + 4y = 2x – 8
• Table
• Graph find the slope and y-intercept for each line
x y = x + 4
2
4
6
x y = 2x - 8
2
4
6
Practice
• Your company wants to print some flyers for advertising a new product. The printer has two options to produce the flyers, The traditional printing cost is $250 for setup and $0.15 per page printed. To print the flyers digitally, they charge $50 for setup and $0.20 per printed page.
Types of Systems
Consistent Inconsistent
Algebraic Methods of solving systems
• Substitution
y = 4x –5
y = x + 22
Replace the expression of a variable in one equation into another.
Substitution
• Geothermal and wind energy, find the year when the amount of geothermal and wind energy produced will be the same.
G(t) = -0.08t + 5.68
W(t) = 0.82t – 1.03