“THE LINEAR FUNCTION CONNECTION”
A LINEAR FUNCTION can be represented in any of the following ways:
 Verbal Description
The Beta students sold necklaces for $3 each. The money earned, y, is
determined by the number of necklaces sold, x.
 Equation
y = 3x
 Ordered Pairs
(5, ___) (3, ___) (2, ___) (0, ___)
 Table
X Y
 Graph
18
12
6
3
 Rate of Change
6
9
Reminder
THE GRAPH OF A LINEAR
EQUATION IS A LINE AND WE
CAN FIND THE SLOPE OF THE
LINE:
or
ALSO, KNOWN AS THE
RATE OF CHANGE!
SOMETIMES, WE NEED TO COMPARE TWO DIFFERENT FUNCTIONS
WHICH ARE REPRESENTED DIFFERENTLY. LET’S TRY THIS!
FUNCTION 1: Susie was playing a game. She could find her answer (y) by multiplying the
number she drew (x) by 2 and then adding 2.
Represent this function as an equation:____________________________
FUNCTION 2: This function is represented with a graph.
Write a sentence that compares the
rate of change for each function.
Greg Greenthumb planted two plants for a science project. The table shows the growth of
Plant 1 over several days.
No. of days (x)
Height in cm (y)
0
1
1.5 3.5
2
3
5.5 7.5
4
9.5
He represented the growth of Plant 2 with the following equation: y = 3 + 1.5x where y is the
height in centimeters over x days.
Write a sentence that compares the rate of growth for the two plants.
USING FUNCTIONS TO CONNECT TO REAL WORLD SITUATIONS
DISTANCE (meters)
1. Billy and his sister Brenda are racing 30 meters to their swimming pool. Billy is younger
so his sister decides to give him a head start of 6 meters. The graph below shows the
distance that Billy runs during the race:
The equation y = 3x can be used to
represent the total distance in meters, y,
that Brenda has run after x seconds.
30
24
18
Determine who is running at a
faster speed. How much faster are
they running?
12
6
2
4
6
8
10
NUMBER OF SECONDS
12
SHOW YOUR WORK IN THE
SPACE BELOW:
2. The Math Madness club is buying t-shirts online. The price of buying x shirts from the
company Math R Us is shown by the graph below. The advertisement shows the cost of
buying the same shirt from Math Print Co. When should the club buy the shirts from
Math R Us? When should the club buy shirts from Math Print Co?
Math R Us
COST IN
DOLLARS
MATH PRINT COMPANY
High Quality Math T-shirts
30
$10 for the first shirt!
22.50
$6 for each shirt after that!
15
7.50
∑
1
2
3
4
NUMBER OF SHIRTS
3. Mallory was given the following equation: y = x + 3 in her math class. Thomas was
given the following table:
x
y
-1
-1
0
3
1
7
2
11
3
15
The teacher asked Sophie to write a
sentence that compares the rate of
change for each of these situations. What
is a correct sentence for Sophie to write?