Terrific Tuesday!

Terrific
Tuesday!
Pick up a copy of the
Warm Up
Answer Sheet and
complete the following
problems. Show your
work!!
**Pick up a copy of
this week’s
Computation from the
front bin.
Direct Variation
• A Direct Variation is a specific relationship in
which there is a constant ratio, (y/x) between
all ordered pairs.
• Direct Variation Equations are written in the
form y = kx.
https://www.khanacademy.org/math/alg
ebra-basics/core-algebra-linearequations-inequalities/core-algebradirect_inverse_variation/v/direct-andinverse-variation
Direct Variation
Finding the
Constant (k)
Identify the constant of the ordered pairs
below. Then, write the equation to represent
the relationship.
1. {(1, 4), (2, 8), (3, 12), (4, 16)}
K = 4 y = 4x
2. {(-6, 3), (-4, 2), (0, 0), (2, -1)}
K=-½
y=-½x
Direct Variation
Identifying
Equations
y = 3x
Identify the equations below that represents a direct variation.
If yes, identify the constant of variation, k.
YES; 3
y = x – 4 NO; it is not in y = kx form
2y = 5x
2 2
y= 5 x
2
YES; 5/2
4x + 2y = 6
-4x
-4x
2y = -4x + 6
2
2
y = -4x + 3
NO
Direct Variation
Identifying
Graphs
A direct variation will create a line through
the origin.
If the equation is y = kx, what is the value of b?
**Use your slope ratio (rise/run) to identify the constant.
Direct Variation
Finding Missing
Values
(2, -4) and (-6, y)
-4 = Y
24 = 2y
2
-6
2
2
If the following ordered pairs represent a
direct variation, find the missing value.
12 = y
y
y
=
x
x
(4, 16) and (x, 24)
16
24
=
4
x
16x = 96
16 16
x=6
Wonderful
Wednesday!
• Complete the
following
problems on
your Warm Up
Answer Sheet.
Show your
work!!
**Pick up a copy
of the
additional
Warm Up from
the front table.
Inverse Variation
• An Inverse Variation is a specific relationship
in which there is a constant product, (x·y),
between all ordered pairs.
• Inverse Variation Equations are written in the
form y = k/x.
Inverse Variation
Finding the
Constant (k)
Identify the constant of the ordered pairs below. Then,
write the equation to represent the relationship.
{(1, 20), (2, 10), (4, 5)}
{(1, -28), (2, -14), (4, -7)}
K = 20 y = 20/x
K = -28 y = -28/x
**TO find the constant, multiply your x and y value by each other.
Graphing Inverse Variation
• If the constant is an inverse variation of 16,
create a table of values to graph the
relationship.
(x · y) = 16
X
Y
1
16
2
8
4
4
8
2
16
1
Plot the points on a
graph after you have
created the table.
**Creates a hyperbola!
Inverse Variation
Finding the
Missing Values
If the following ordered pairs represent an inverse
variation, find the missing value.
xy = xy
(12, 14) and (-24, y)
12 · 14 = -24 · y
168 = -24y
-24 -24
(6, -10) and (3, y)
6 · 10 = 3 · y
60 = 3y
3 3
y = -7
y = 20
RMS Time!
•Come into class quietly and find your designated
seat.
•GO TO YOUR LOCKERS! Get your things for 1st and
5th block. You will have time to go to your lockers
again after 5th block.
•Take out a book or magazine of your own or one of
mine from the back bookshelf and begin reading
silently.
•If possible, complete an RMS Short Sheet. (Copies
can be found in the blue folder by the bookshelf or
on instagram at #rmsshortsheets)
Thankful
Thursday!
• Complete the
following problems
on your Warm Up
Answer Sheet.
Show your work!!
**Pick up a copy of
the “Entrance
Ticket” from the
front table.
**Turn in your
Computation to
the appropriate
bin.
Applications of Direct &
Inverse Variation
When do we use Direct?
When do we use Inverse?
In situations where,
as one variable ,
In situations where,
as one variable
the other variable
The other variable
Direct Variation Applications
The sales at a baseball game vary directly with the number of
people attending. If the sales for a game are $12,000 when
800 people attend, determine how many people attend if the
sales for a game are $15,000?
Use the ratio
y/x = y/x
Code Words: sales, # of people (these are your terms)
vary directly->tells you how to set up
y = sales
x = # of people
12,000 = 15,000
800
x
12,000x = 12,000,000
12,000
12,000
x = 1,000 people
Direct Variation Applications
Ounces of medication vary directly with the weight of the
patient. If a 120 lb. adult requires three-fourths of an ounce of
medication, how many ounces are required for a 200 lb. adult?
Use the ratio
y/x = y/x
Code Words: ounces, weight (these are your terms)
vary directly-> tells you how to set up
y = ounces
x = weight
0.75 = y
120 200
120y = 150
120 120
y = 1.25 oz.
Inverse Variation Applications
Time traveling varies inversely with the average speed. If a
train travels between two cities in 3 hours at an average speed
of 65 miles per hour, how long would it take at an average of 78
miles per hour?
Use the ratio
xy = xy
Code Words: time, avg. speed (these are your terms)
varies inversely-> tells you how to set up
y = time
x = average speed
3 · 65 = 78y
195 = 78y
78 78
y = 25 hours
Inverse Variation Applications
A company that produces laptops has determined that the
number of laptops it can sell varies inversely to the price of the
laptop. Two thousand laptops can be sold when the price is
$2500. How many laptops can be sold if the price of the laptop
is $1000?
Use the ratio
xy = xy
Code Words: # of laptops, price (these are your terms)
varies inversely-> tells you how to set up
y = # of laptops
x = price
2000(2500) = 1000y
5000000 = 1000y
1000
1000
y = 5000 laptops