Sections 2-5

1
Sections 2-5 8-1

• Direct Inverse Variations

2
Objectives

• I can recognize and solve direct variation word
  problems.
• I can recognize and solve inverse variation word
  problems

3
Direct Variation
As one variable increases, the other must also
increase ( up, up) OR As one variable decreases,
the other variable must also decrease. (down,
down)
4
Real life?

• With a shoulder partner take a few minutes to
  brainstorm real life examples of direct
  variation. Write them down.

Food intake/weight Exercise/weight loss Study
time/ grades Hourly rate/paycheck size Stress
level/blood pressure Recipes Paint Mixtures Drug
Manufacturing
5
Direct Variation

• k is the constant of variation
• the graph must go through the origin (0,0) and
  must be linear!!

6
K Constant of Variation

• What does K really represent in direct variation??

7
Direct Variation
Ex 1)If y varies directly as x and y 12
when x 3, find y when x 10.
8
Solving Method 1
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Solving Method 2
10
What did we do?
EITHER ONE WILL WORK!! ITS YOUR CHOICE!
11
Direct Variation Application

• Ex In scuba diving the time (t) it takes a
  diver to ascend safely to the surface varies
  directly with the depth (d) of the dive. It
  takes a minimum of 3 minutes from a safe ascent
  from 12 feet. Write an equation that relates
  depth (d) and time (t). Then determine the
  minimum time for a safe ascent from 1000 feet?

12
Your TURN 1 on Homework

• Find y when x 6, if y varies directly as x and
  y 8 when x 2.

13
Inverse Variation
As one variable increases, the other decreases.
(or vice versa)
14
Inverse Variation

• This is a
• NON-LINEAR function (it doesnt look like
  ymxb)
• It doesnt even get close to (0, 0)
• k is still the constant of variation

15
Real life?

• With a shoulder partner take a few minutes to
  brainstorm real life examples of inverse
  variation. Write them down.

Driving speed and time Driving speed and gallons
of gas in tank Pressure versus Volume Water Depth
versus Time of dive
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Inverse Variation
Ex 3) Find y when x 15, if y varies inversely
as x and when y 12, x 10.
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Solving Inverse Variation
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Method 2
19
What did we do?
EITHER ONE WILL WORK!! ITS YOUR CHOICE!
20
Inverse Variation Application
ExThe intensity of a light I received from a
source varies inversely with the distance d
from the source. If the light intensity is 10
ft-candles at 21 feet, what is the light
intensity at 12 feet? Write your equation first.
21
Your TURN 2 on Homework
Find x when y 5, if y varies inversely as x and
x 6 when y -18.
22
½ Sheet Data

• Examine the data that you have comparing two
  variables.
• Determine if the data varies directly or
  inversely or neither.
• After determining the type of variation, find the
  constant of variation and answer the question.

23
Group Work

• Get into groups based on your question number.
• Compare the answers that you each found and be
  prepared to present finding to the class.
• You will present under the document camera

24
Direct vs. Inverse Variation
25
Homework

• WS 1-3
• Quiz next class on Parent Functions