Name ____________________________
Chapter 5 Lesson 6
Math 8 Topic: Writing Linear Function Rules DO IT:
What you have to leave
here knowing:
1) Thalcundra is 3 x 108 miles away from the sun while
Perelandra is 7 x 1011 miles away from the sun. About
how many times further away from the sun is Perelandra?
1) Write a function rule
based on a table.
a) 20
2) SWRL….. Interpret.
Connect. “Write a
function rule.”
2) What is the slope of the line connecting (-2, 3) and
(0, 7)?
b) 200
c) 2,000
d) 20,000
3) What is the equation of a line whose slope is -2 and y – intercept is 5?
a) y = -3x + 2
b) y = 2x – 3
c) 2y = -x
d) -3y = 9x
4) Which of the following is a solution to the inequality 3n + 5 < 11
a) 1
b) 2
c) 3
d) -1
5) In the function y = -2x – 5, what is the output if the input is 9?
SELECT HOMEWORK ANTZAS:
We will do select questions at the board.
TODAY’S LESSON
Which of the following are NOT functions;
a) {(1, 3) (5, 7) (7, 15)}
b) {(1, 3) (2, 7) (3, 7)}
c)
d)
TODAY’S LESSON:
For linear patterns, there is a constant rate of change. This rate of change (I hope you
remember) is called slope. If we also remember that y = mx + b takes the form of a
function rule, we can write function rules by finding m and b in a table.
Here are three examples I will do with you.
x
0
1
2
3
4
y
3
5
7
9
11
__________________
t
0
25
50
75
100
p
50
150
250
350
450
________________
x
-2
-1
0
1
2
f(x)
-11
-7
-3
1
4
_____________
TEAM WORK: Now you do the same thing with a partner. Find the missing value
while you are at it ☺.
x
0
1
2
3
4
y
-2
5
12
19
__________________
t
0
25
50
75
100
p
40
125
210
295
380
________________
x
-2
-1
0
1
2
g(x)
-4
-2
0
2
4
_____________
INDIVIDUAL WORK: (If you are really stuck and can’t start this yourself, you may turn
to a neighbor for help.)
Jeremy went on a conditioning program. As part of that program, he began riding his
bike long distances. Each week increased by the same amount. After 2 weeks, he
rode 17 miles daily. After 3 weeks, he rode 21 miles a day. At 4 weeks, he had
increased to 25 miles each day. At the fifth week, Jeremy was riding 29 miles per day.
1) Summarize the data by placing it in the table below.
Week
Miles
2) We are going to write a function rule …… but his will take some figuring first.
Remember, we always want to get the data into y = mx + b form. The problem here is
that the table does NOT show a “0”, so we can’t pair up a y – intercept.
Can you figure out a way to find the y – intercept?
Write the function rule: ___________________________________
THE HAPPY RECAP
In a linear relationship, you need to find the slope and the ____________________.
How do you find this? _________________________________________________.
How do you find the slope?
Available Internet Resources:
Khanacademy.com
My website:
http://pages.pmschools.org/sites/rlindquist/Mr._Lindquists_Math_Land/Daily_Math_Blo
g/Daily_Math_Blog.html
HOMEWORK:
1) Solve for the variable in the equation or inequality below.
a) 7(x + 5) + 2x = 8
b) -2n - 3n - 6 > 14
Is 4 a solution to the above question? ______
2) One number is five less than twice another number. The sum of the numbers is 28.
Find the larger number.
3) Review Work. Simplify each.
a) (7w3z7 )(8w2z)
b) (8 x 107)(9 x 1021)
e) 3n2 – 5n + 4 + n2 – 2n – 6
c)
! ! !"!!
! ! !"!!
d) 7w3 - 9w3
f) 7a – 5b – (3a – 8b)
4)
!
a) What are the slope and y – intercept of the line y = ! x + 5?
b) What are the slope and y – intercept of the line y + x = 2?
c) What are the slope and y – intercept of y = 5?
d) What are the slope and y – intercept of x = 4?
e) Write the equation of a line parallel to y = 5x – 4 but with the same y – intercept as
3y – 4x = 12.
!
5) A line has a slope of !. It passes through the points (1, 3) and (3, y). What is the
value of y? (Use of the graph above is optional.)
6) If y = ½ x + 4, find the output if x = -10.
7) If f(x) = 11 – 3x, find f(-3).
8) Which of the following is not a linear function?
a) y – x = 5
b) y = x2 + 8
c) x + 4x – 3 = y
d) y = 2(x – 1)
9) Which of the following is not a function and why?
a) {(1, 5) (2, 5) (3, 7) (3, 9)}
b) {(1, 3) (2, 4) (3, 4) (4, 4)}
10)
y= 𝑥+1
Complete the table of values and list as a set of ordered pairs.
x
0
1
4
9
100
y
11) Jenny wants to start a business making websites. It costs her $70 for a license
and $820 for supplies. Each website she creates earns her a profit $175.
Which variable is the input? _____ Which is the output? ______
Write a function rule that shows how much profit (p) Jenny earns with teach website
(w) created.
Complete a table below that shows how much profit is earned for the given number of
websites created.
w
0
1
2
3
8
p
12) How many websites does Jenny have to sell in order to turn a profit (this means a
positive amount of money is made.)
13) What is Jenny’s profit if she creates 30 websites?
14) Jenny needs a profit of $1,500.00 in order to hire an assistant. How many
websites does Jenny need to create in order to hire an assistant?
15) Todd needs to create a function finds the perimeter of an octagon (P) based on
the length of a side (s). {An octagon has 8 sides.}
Complete the table below.
s
1
2
3
4
5
P
16) If the length of a side is 14, what is the perimeter of the hexagon?
17) If the perimeter of a hexagon is 96, what is the length of a side?
18) Write a function rule for finding the perimeter of an octagon. ________________
<<<<< KEEP GOING ……… JUST A COUPLE MORE >>>>>
19) Write a function rule for each and find any missing values.
x
0
1
2
3
4
y
-5
-2
1
4
__________________
t
0
20
40
60
120
p
35
75
115
155
________________
x
-2
-1
0
1
2
g(x)
-3
2
7
12
_____________