Warm Up
Solve for y.
1.
3 + y = 2x
2.
6x = 3y
Write an equation that describes the relationship.
3.
Solve for x.
4.
5.
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Algebra/Lesson 4-5: Direct Variation
Objectives:

Identify, write, and graph direct variation.
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.
The equation y = 5x describes this relationship. In this relationship, the number of servings varies directly with the number of cups of
rice.
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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 1:
A.
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.
B.
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.
C.
Tell whether the equation represents a direct variation. If so, identify the constant of variation.
C.I.O.-Example 1: Tell whether the equation represents a direct variation. If so, identify the constant of variation.
a.
3y = 4x + 1
c.
y + 3x = 0
b.
3x = –4y
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What happens if you solve y = kx for k?
So, in a direct variation, the ratio
𝑦
𝑥
𝑦
𝑥
is equal to the constant of variation. Another way to identify a direct variation is to check whether
is the same for each ordered pair (except where x = 0).
Example 2: Tell whether the relationship is a direct variation. Explain.
A.
B.
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C.I.O.-Example 2: Tell whether the relationship is a direct variation. Explain.
a. Method 2
b. Method 1
c. Method 2
Example 3:
The value of y varies directly with x, and y = 3, when x = 9. Find y when x = 21.
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C.I.O.-Example 3:
The value of y varies directly with x, and y = 4.5 when x = 0.5. Find y when x = 10.
Method 1: Find the value of k and then write the equation.
Method 2: Use a proportion.
Example 4:
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.
C.I.O.-Example 4b:
The perimeter y of a square varies directly with its side length x. Write a direct variation equation for this relationship. Then graph.
Step 1: Write a direct variation equation.
Step 2: Choose values of x and generate ordered pairs.
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Step 3: Graph the points and connect.
Lesson Quiz: Part I
Tell whether each equation represents a direct variation. If so, identify the constant of variation.
1.
2y = 6x
2.
3x = 4y – 7
Tell whether each relationship is a direct variation. Explain.
3.
4.
Lesson Quiz: Part I
5. The value of y varies directly with x, and y = –8 when x = 20. Find y when x = –4.
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6. Apples cost $0.80 per pound. The equation y = 0.8x describes the cost y of x pounds of apples. Graph this direct variation.
p. 265: 10-15, 17-19, 21, 23, 27, 37
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