I
received a flyer in the mail from a
landscaping company that maintains lawns in
my area.
 They charge $5 for the use of their
equipment and then $4 per hour to cut and
trim the grass.
 Independent variable: # of hours it takes
 Dependent variable: the amount I must pay $
 Rate of Change: $4 per hour
Number of
hours
0
1
2
4
Cost $
5
9
13
21
The table of values will have a “initial
value or starting cost”. This is the value of
y when x=0
In our situation, the initial value is = to 5
The initial value has a symbol “b”
The table of values is NOT
PROPORTIONAL…means you cannot cross
multiply to get the same answer.
 The
line of the graph does not go
through the origin.
 The line starts above or below the
origin
 The line starts at the initial value
“b” and then goes in a straight line.
Cost
22
20
18
16
14
12
10
8
6
4
2
-
•(4,21)
•(2,13)
•(1,9)
1
2
Initial value is where
the line crosses the y
axis
3
4
Number of hours
The initial value is also
called the y-intercept

rule looks like this:
y = ax + b
dep = (r.o.c)(indep var) + initial value
 Rule
for our situation
y = 4x + 5
y = 5 + 4x
 Workbook
 Page
110-11 activity 4
 Page 117 #10 and #11
 Page 118 #12
 Textbook
#2 direct and partial questions
 Direct: page 102 #4,5

103 #6,7
 Partial page 117 #4..find r.o.c. and then
write the rule y=ax +b
 Workbook
is your HOMEWORK
 Page 117 #10 and #11
 Page 118 #12
 Textbook
#2 IS NOT HOMEWORK
 page 117 #4..step 1 find r.o.c. “a”
step 2 find initial value “b”
step 3 write the rule y=ax +b
 Workbook
 Page
117 #10 and #11
 Page 118 #12
 Textbook

#2
Page 115 #1 a-h
 page
117 #4a-e..step 1 find r.o.c. “a”
step 2 find initial value “b”
step 3 write the rule y=ax +b
X
1
2
4
6
y
5
6
8
10
Remember: the rule “looks” like y = ax + b
Step 1: find the rate of change
(1,5) (2,6)
x 1 y1
x 2 y2
a = 6-5
2-1
a=1
 Step
2: find the initial value “b”
y = ax + b
you need to pick 1 of the coordinates
to substitute into the rule (1,5)
x,y
5 = 1(1) + b
5=1+b
5–1=1+b-1
4 = b now put it back into the rule
 So
far you have a = 1 and b = 4 that’s all you
need to do this !!!
 Rule
y = 1x + 4
Try the following example..follow the pattern
X
30
40
y
560
680
 Step
1- find “a’”
( 30,560) (40,680)
x 1 y1
x 2 y2
a = 680-560
40-30
a = 120
10
a = 12
 Step
2- find the “b”
pick a coordinate (30,560)
x
y
Y = ax + b
560 = 12(30) + b
560 = 360 + b
560 – 360 = 240 + b -360
b = 200
Write the rule
y = 12x + 200
1-
( 3,15) and (-2,-5)
2- (2,2) and (-5,23)
3- (6,38) and (11,53)
 Follow
all the steps like in your notes.
Answers
1- y=4x+3
2- y=-3x +8
3- y=3x +20
 On
the graph look to see if the line passes
through the y-axis at point that you know.
in this case you know
3
that the b=3.
 Pick the coordinates of the initial value (0,3)
and then 1 other point. Use these 2 points to
calculate “a”.
 Once you have calculated “a” you can write
out the rule in the form of y=ax+b
 On
the graph, pick two points that are
definitely on the line.
 Find the rate of change
 Follow the steps for finding the rule for
partial based on a table of values
 Workbook
homework
 Page 121 #3-7
Not for homework but work on it if you finish
the above
 Page 112 #1,2
 Page 113 #3,4,5
 Page 114#5,6
 Workbook
homework
 Page 121 #3-7
 Page 112 #1,2
 Page 113 #3,4,5(use -1,0,1 as x values in the
table of values)
 Page 114#5 continued
Write the equation of the line that passes
through the following points.
Be sure to show all work required…neatly.
a)(3,-2) and (4,0)
Y = 2x – 8
c) (1,2) and (3,-2)
Y = -2x +4
e) (4,1) (12,5)
Y = 0.5x -1
b) (7,-4) and (4,5)
Y = -3x +17
d) (9,4) and (10,-2)
Y = -6x +58
(3,-2) ( 4,0)
x1y 1 x2 y2
Find “a”= 0 – (-2)
4-3
a=2
1
a=2
Find “b” y = ax + b
0 = 2(4) +b
0=8+b
0-8 = 8 + b – 8
-8 = b
Write the rule y = ax + b
y = 2x - 8
Homework 4306
Finish the 5 questions (finding
equation or rule)
Textbook #2 page 119 #13
page 120 #16
page 125 #32
Expect an assessment on finding the
rule on Wednesday or Thursday
91’s
workbook
Page 112 #1,2
Page 113 #3,4,5
Page 114#5 continued #6