Unit 2: 3 Direct Variation
2015-2016: Algebra I CP
Write and graph direct variation equations
GOAL(S):
Identify direct variation equations
You work for Amazon in their warehouse. You’re a team member on a project to determine optimal procedures for
stacking boxes for packaging and shipping. Each box is 10 cm high.
THIS
VS
THIS
(1.) Create a table and complete the graph.
x
# of boxes
y or f(x)
height of
stack
0
1
2
3
4
5
6
7
(2.) Write the function.
(3.) Determine the domain and the range
Page 1 of 6
Unit 2: 3 Direct Variation
2015-2016: Algebra I CP
The number of boxes is DIRECTLY PROPORTIONAL to the height of the stack.
** relationship in which the ratio of one quantity to another remains constant **
(4.) Use a proportion to determine the height of a stack of 12 boxes.
When two values are directly proportional, there is a DIRECT VARIATION.
In terms of stacking boxes, the height of the stack varies directly as the number of boxes.
y varies directly as x
Direct variation is defined as y = kx, where k ≠0
and the coefficient k is the CONSTANT OF VARIATION.
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Unit 2: 3 Direct Variation
2015-2016: Algebra I CP
EXAMPLE
NON-EXAMPLE
x
-2
-1
1
2
x
-2
-1
1
2
y
-4
-2
2
4
Y
-5
-3
1
3
2
2
2
2
k
5
2
3
1
3
2
k
y
x
y  2x
y
x
y  2x 1
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Unit 2: 3 Direct Variation
2015-2016: Algebra I CP
(5.) Is the graph a direct variation? Justify your answer.
(6.) Is the graph a direct variation? Justify your answer.
(7.) Is the table a direct variation? Justify your answer.
(8.) Is the table a direct variation? Justify your answer.
x
y
x
y
0
4
0
0
4
10
4
6
10 19
(9.)
Is the table a direct variation? Justify your answer.
10 15
(10.) Is the table a direct variation? Justify your answer.
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Unit 2: 3 Direct Variation
(11.) Is the equation y = 5x a direct variation? Justify your
answer.
2015-2016: Algebra I CP
(12.) Is the equation y = 5x – 2 a direct variation? Justify
your answer.
(13.) The value of y varies directly with x and the constant
(14.) The value of y varies directly with x and the constant
of variation is 7. What is the value of x when y = 63?
of variation is 12. What is the value of y when x = 5?
(15.) Write the direct variation equation. x is 45 when y is 5
(16.) Write the direct variation equation. y is 6 when x is 5
Page 5 of 6
Unit 2: 3 Direct Variation
2015-2016: Algebra I CP
(17.) The height y of a stack of boxes varies directly as the number of boxes x. If we pile 25 boxes it will be 500 cm high.
a. Find the constant of variation.
b. Write the direct variation equation.
c. If we have 20 boxes, what is the height of the boxes?
WORK AREA
(18.) At the packaging and shipping company, you get paid each week. One week you earned $48 for 8 hours of work.
Another week you earned $30 for 5 hours of work.
a. Write a direct variation equation that relates your wages to the number of hours you worked each
week.
b. Explain the meaning of each variable and identify the constant of variation.
c. How much would you earn if you worked 3.5 hours in one week?
WORK AREA
(19.) A grocery store sells 6 oranges for $2. Round to the nearest cent if necessary.
a. Write a direct variation equation that relates your wages to the number of hours you worked each
week.
b. Explain the meaning of each variable and identify the constant of variation.
c. How much would 10 oranges cost?
WORK AREA
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