Download 5.6 Direct Variation Notes.notebook

5.6 Direct Variation Notes.notebook
Algebra Lesson 5.6
Today's learning target:
December 17, 2013
A recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a chef needs 1 cup of rice for every 5 servings. Students will be able to identify, write, and graph direct variation.
The equation y = 5x describes this relationship. In this relationship, the number of servings varies directly with the number of cups of rice.
MN Standards: 7th Grade Standard (previous course) Example 1A:
Identifying Direct Variations from Equations
Tell whether the equation represents a direct variation. If so, identify the constant of variation.
y = 3x
This equation represents a direct variation because it is in the form of y = kx. The constant of variation is 3.
A direct variation is a special type of linear relationship that can be written in the form y = kx, where k is a nonzero constant called the constant of variation.
Example 1B:
Tell whether the equation represents a direct variation. If so, identify the constant of variation.
3x + y = 8
This equation is not a direct variation because it cannot be written in the form y = kx.
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5.6 Direct Variation Notes.notebook
Example 1C:
Tell whether the equation represents a direct variation. If so, identify the constant of variation.
December 17, 2013
Try It Out!
Tell whether the equation represents a direct variation. If so, identify the constant of variation.
3y = 4x + 1
3x = –4y y + 3x = 0 What happens if you solve y = kx for k?
Example 2A: Identifying Direct Variations
from Ordered Pairs
Tell whether the relationship is a direct variation. Explain.
Method 1 Write an equation.
y = 3x
This is direct variation because it can be written as y = kx, where k = 3.
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5.6 Direct Variation Notes.notebook
December 17, 2013
Try It Out!
Example 2a
Tell whether the relationship is a direct variation. Explain. Example 2B:
Tell whether the relationship is a direct variation. Explain.
Method 1 Write an equation.
y = x – 3 This is not a direct variation because it cannot be written as y = kx.
Example 2b
Tell whether the relationship is a direct variation. Explain. Example 2c
Tell whether the relationship is a direct variation. Explain. Example 4: Graphing Direct Variations
A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph.
Example 3: Writing and Solving Direct
Variation Equations
Step 1 Write a direct variation equation.
The value of y varies directly with x, and y = 3, when x = 9. Find y when x = 21. Method 1 Find the value of k and then write the equation.
Step 2 Choose values of x and generate ordered pairs.
Method 2 Use a proportion.
Step 3 Graph the points and connect.
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5.6 Direct Variation Notes.notebook
December 17, 2013
Algebra Lesson 5.6
Today's learning target:
Students will be able to identify, write, and graph direct variation.
HW: 5.6 #10-17, 20-44 evens,
47-55 p339-341
MN Standards: 7th Grade Standard (previous course) 4