Ch 7

1
Ch 7

• Section 7 Direct and Inverse Variation

2
Review

• Ratios are comparisons between two values.
• Proportions are equations showing that ratios are
  equal to one another.

3
Review

• Proportions are used to compute how a change in
  one quantity affects the related quantity.

This year 11 out of 24 Criminal Justice students
are from Grant County. There are 35 new
students signed-up for next years program. How
many of the new students do you predict will be
from Grant County?
x 16
4
Direct Relationships

• Two items are related.
• An increase in one item leads to an increase in
  the other.
• A decrease in one item leads to a decrease in the
  other.

Price
Quantity
5
Using Equations of Direct Variation

• 3 items for 1.90
• 7 items for ???

Unit Price

• Hidden Number ___________

0.633
Total Cost ? Quantity

• Equation Total Cost Unit Price ? Quantity

variation constant or constant of proportionality
6
The Language of Direct Variation
y kx

• Direct Variation
• y is directly proportional to x.
• y varies as x.
• y is proportional to x.

7
Solve Using Direct Variation Equation

• 3 items for 1.90
• 7 items for ???

Cost is directly proportional to quantity.
c kq
c 0.633q
y kx
c kq
1.90 k(3)
c 0.633(7)
3
3
c 4.43
0.633 k
0.633
8
Example

• Write an equation of variation in which y varies
  directly as x and y 20 when x 4.

y 5x
y kx
What is the value of y when x is 32?
What is the value of x when y is 90?
20 k(4)
90 5x
y 5(32)
5 k
y 160
x 18
9
Application Lunar Weight

• The weight M of an object on the moon varies
  directly as its weight E on earth.
• Someone who is 192 lb on earth would weigh only
  32 lb on the moon.
• If a person weighs 120 lb on earth, what would
  their weight be on the moon?

M 0.167E
M kE
M 0.167(120)
32 k(192)
M 20 lb
0.167 k
10
Inverse Relationships

• Two items are related.
• An increase in one item leads to an decrease in
  the other.
• A decrease in one item leads to an increase in
  the other.

Time
Speed
11
The Language of Inverse Variation

• Inverse Variation
• y is inversely proportional to x.
• y varies inversely as x.

12
Application of Workers

• The length of time to complete a basic robbery
  investigation is inversely proportional to the
  number of detectives assigned to the case.
• The most recent business robbery took 13 days to
  solve when 3 detectives were assigned.
• How long would it have taken to solve if 5
  detectives were assigned?

13
Application Filling Time

• The time t required to fill a pool varies
  inversely as the rate r of flow into the pool.
• A tanker can fill a pool in 90 min at the rate of
  1200 L/min.
• How long would it take to fill the pool at a rate
  of 225 L/min?

k 108,000 and t 480 min when flow
rate is 225 L/min.
14
Practice

• Write an equation of variation in which y varies
  inversely as x and y 45 when x 2.

This is the equation of variation.
15
Practice

• MathXL Ch 7 Section 7 Homework
• Ch 7 Practice Test
• Ch 7 Graded Test (Thursday)