7­4 direct variation equations.notebook
Daily Do from last class
February 02, 2017
Homework Answers 7­3:
What is the rate of change for this graph?
Your Name
Lesson 7­4
Mrs. T
1/ /17
Notes
Rate of change
and Direct Variation
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7­4 direct variation equations.notebook
February 02, 2017
Objective: To be able to find the constant rate of change for a linear function and interpret its meaning. To be able to determine whether or not a proportional relationship exists between two quantities.
Virtue/Skill: Direct variation and slope are very similar. If you can graph a linear function understanding the rate of change, you will be able to graph a line using the slope and y­intercept.
When you see a straight line on a graph.
Linear Relationship It has a constant rate of change
constant rate
Direct Variation
constant rate
NOT a constant rate
A special type of linear equation that describes the rate of change. It is a proportional linear relationship.
*passes through the origin, *nothing added or subtracted
expressed by y = kx k= constant of variation
k is found by dividing y by x
the ratios will be the same for every pair of values.
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7­4 direct variation equations.notebook
February 02, 2017
Do these examples have a constant rate of change?
Are they examples of direct variation?
Are they proportional linear relationships?
Is it a PROPORTIONAL Linear relationship?
# of people
(x)
cost of parking (y)
1
2
3
4
$4
$8
$12
$16
# of people
(x)
cost of parking (y)
constant rate, constant ratios proportional?
1
2
3
$13
$22
$31
4
constant rate,
$40 constant ratio
proportional?
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7­4 direct variation equations.notebook
February 02, 2017
Direct variation y= kx ­­just find k... the rate of change y/x
­­place k into the equation
Write an equation describing the amount of information burned onto a CD and the time it takes to burn it.
Amount of info
(megabytes)
Time (seconds)
2.5
10
3.75
15
10
40
25
100
Constant Ratio= 0.25mb
1 second
Interpret its meaning
0.25 megabytes is burned onto a CD in 1 second
equation y = 0.25x or y = 1/4x
­­Use the equation to find how many megabytes are burned in 8 seconds.
y=.25x
Write a direct variation equation that relates cost and weight. Find the rate of change (k)
Interpret its meaning
Write an equation that could be used to find the cost of x amount of weight
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7­4 direct variation equations.notebook
February 02, 2017
Lets look at page 379 in your textbook.
#1
#2
interpret the meaning of each rate of change
Write a direct variation equation for each graph.
Summary
Objective: To be able to find the constant rate of change for a linear function and interpret its meaning. To be able to determine whether or not a proportional relationship exists between two quantities.
Virtue/Skill: Direct variation and slope are very similar. If you can graph a linear function understanding the rate of change, you will be able to graph a line using the slope and y­intercept.
Assignment: Workbook 7­4
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7­4 direct variation equations.notebook
February 02, 2017
Exit Question
Is it proportional or an example of direct variation? Explain
What is the k?
What is the equation for this linear relationship?
Warm Up
1­ Find 4 solutions for the equation.
y= ­3x
2­ 10 is what percent of 50?
3­ Find 95% of 256.
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