Unit 4 Section 9 Rate of Change Direct Variation.notebook
February 03, 2016
Feb 12­8:31 AM
Feb 12­8:31 AM
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Unit 4 Section 9 Rate of Change Direct Variation.notebook
February 03, 2016
Feb 12­8:50 AM
Rate of Change
Unit 4
Jan 28­1:53 PM
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Unit 4 Section 9 Rate of Change Direct Variation.notebook
February 03, 2016
Vocabulary
Rate of Change:
**The same as SLOPE!!!**
y
x
Jan 28­1:53 PM
Example 1: Find the rate of change. Explain what the rate of change means.
Cost (dollars)
Cost of Movie Tickets
60
55
50
45
40
35
30
25
20
15
10
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Tickets
Jan 28­1:55 PM
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Unit 4 Section 9 Rate of Change Direct Variation.notebook
February 03, 2016
Example 2: Find the rate of change for the table. Graph the data.
Time (h) Distance Flown (mi)
x
y
0
0
2
1000
4
2000
6
3000
8
4000
Jan 28­1:57 PM
Example 3: State the independent and dependent variable in each linear
relationship. Then find the rate of change for each situation.
A) Snow is 2 in deep after 1 h and 6 in deep after 3h
B) The cost of tickets is $36 for three people and $84 for seven people
C) A car is 200 mi from its destination after 1 h and 80 mi from its
destination after 3 h.
Dec 30­11:52 AM
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Unit 4 Section 9 Rate of Change Direct Variation.notebook
February 03, 2016
Direct Variation
Direct Variation: a function in the form y= kx, where k ≠ 0. y = k
x
k is the constant of variation!!
Dec 30­12:08 PM
Example 4:
Suppose y varies directly with x, and y = 35 when x = 5. What direct variation equation relates x and y? What is the value of y when x = 9?
y = kx
Start with the function form of a direct variation.
35 = k(5)
Substitute 5 for x and 35 for y.
7 = k
Divide each side by 5 to solve for k.
y = 7k
Write an equation. Substitute 7 in for k in y = kx.
The equation y = 7k relates x and y. When x = 9, y =7(9), or 63.
Dec 30­12:15 PM
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Unit 4 Section 9 Rate of Change Direct Variation.notebook
February 03, 2016
Suppose y varies directly with x. Write an equation relating x and y.
5) y = ­6 when x = ­2
6) y = ­27 when x = 9
7) y = 4 when x = 16
8) y =48 when x = ­4
Dec 30­12:19 PM
Homework:
page 29, 30
Jan 31­12:03 PM
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Unit 4 Section 9 Rate of Change Direct Variation.notebook
February 03, 2016
Jan 31­12:19 PM
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