Sequences  Linear Functions OBJ: Connect arithmetic sequences to linear functions UNIT TWO DAY 2.5

 The position of terms is the domain  The value of terms is the range  Common difference = Rate of change = Slope  On a linear graph, rate of change is called slope  The first term is not the y-intercept OBJ: Connect arithmetic sequences to linear functions CONNECTIONS

OBJ: Connect arithmetic sequences to linear functions FORMULAS FOR WRITING LINEAR MODELS

OBJ: Connect arithmetic sequences to linear functions WRITE AN EXPLICIT RULE

 The sequence 50, 55, 60, 65, … describes Tom’s pay for making geometric mobiles.  Make a table for the given information.  Choose two points to find slope and find b.  Write your equation in slope-intercept form. OBJ: Connect arithmetic sequences to linear functions TRY USING SLOPE-INTERCEPT FORM

 What does the rate of change represent?  What does the y-intercept represent?  Is the domain discrete or continuous?  How do sequences compare to linear functions? How does it all relate? OBJ: Connect arithmetic sequences to linear functions SEQUENCES VS. FUNCTIONS

 The sequence 2, 4, 6, … describes the number of dancers in each row of a formation.  Write a linear model to fit the situation. OBJ: Connect arithmetic sequences to linear functions DANCE CLASS

Rate of change describes how one quantity changes in relation to another quantity.  Is the rate of change constant in a linear function?  What does this mean? OBJ: Connect arithmetic sequences to linear functions LINEAR RATE OF CHANGE

 Your gym membership costs $33 per month after an initial membership fee. You paid a total of $228 after 6 months.  Make a table that represents the sequence.  Write an equation that gives the total cost as a function of the length of your gym membership (in months). OBJ: Connect arithmetic sequences to linear functions GYM MEMBERSHIP

 A radio station charges a fee for the first minute of an ad and $125 for each additional minute. You paid $750 for a 4 minute ad.  Make a table that represents the sequence.  Write an equation that gives the total cost (in dollars) to run an ad as a function of the number of minutes the ad runs. OBJ: Connect arithmetic sequences to linear functions RADIO FEES

In BMX racing, racers purchase a one year membership to a track. They also pay an entry fee for each race at that track. One racer paid a total of $125 after 5 races. A second racer paid a total of $170 after 8 races. A.Make a table that represents the information. B.Write an equation to model the situation. C.Describe the slope and the y-intercept in the context of the problem. OBJ: Connect arithmetic sequences to linear functions BMX RACING

 A ranch offers groups the opportunity to visit a working ranch for one day and night for different numbers of people. They charge $250 for a group of 4 people and $350 for a group of 6 people.  Make a table that represents the information.  Write an equation that gives the cost as a function of the number of people in the group. OBJ: Connect arithmetic sequences to linear functions CHECKPOINT