Linear Models YearPopulation (millions) 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 axis L2 represents y or vertical axis  Go to L1 and enter the values  Go to L2 and enter the values on the table

Linear Models: TI –84 Domain/Range Select WINDOW and you will see: Xmin = smaller than smallest input Xmax= larger than largest input Xscal= Ymin= smaller than the smallest output Ymax= larger than largest output Yscal= Each will be based on the domain and range of the values from the table.

Linear Models: TI –84 Graphing Points Enter 2 nd and y = A screen with STAT PLOTS 1:Choose 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 – m = (round to nearest hundredth) Y-intercept y = 0.16x + b 8.41 = 0.16(3) + b 8.41 = b 7.93 = b

Graphing Line on TI- 84 y = 0.16x Select y =, button Enter the equation found 0.16x Use the X,T,,n button to insert x into the equation. Once the equation is entered select GRAPH A 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 YearRevenue (Billions $)

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)} InputOutput xy

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 weekMondayWednesdaySaturdayMonday Temperature F

Notation f(x) “f of x” Represents a function named f that depends on the variable x f 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 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. YearPopulation (millions)

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 + 4 y = 2x – 8 Table Graph find the slope and y-intercept for each line xy = x xy = 2x

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 W(t) = 0.82t – 1.03