Transcript Warm-Up

UNIT TWO
DAY 2.5
OBJ: Connect arithmetic sequences to linear
functions
Sequences 
Linear
Functions
CONNECTIONS
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
FORMULAS FOR WRITING LINEAR MODELS
Slope:
𝑦2 −𝑦1
𝑥 2 −𝑥 1
Slope-Intercept: 𝑦 = 𝑚𝑥 + 𝑏
Point-Slope: 𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
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.
 Write an explicit rule for the sequence.
 How does this compare to slope-intercept
form? 𝑦 = 𝑚𝑥 + 𝑏
OBJ: Connect arithmetic sequences to linear
functions
TRY USING SLOPE-INTERCEPT FORM
 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
 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?
OBJ: Connect arithmetic sequences to linear
functions
SEQUENCES
VS.
FUNCTIONS
How
does it
all
relate?
DANCE CLASS
 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
LINEAR RATE OF CHANGE
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
GYM MEMBERSHIP
 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
RADIO FEES
 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
BMX RACING
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
CHECKPOINT
 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