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WorksheetsProportional vs NP Review
Total questions: 190
Worksheet time: 5hrs 42mins
y = 75x
y= 3.75x + 2
y = 75x
What type of relationship is a direct variation.
proportional
non-proportional
What does "k" stand for in the direct variation equation?
constant of equality
constant of proportionality
constant of non-proportionality
What is another name for constant of proportionality?
constant of non-proportionality
constant of equality
constant of variation
Which of the following is the equation format for direct variation?
y = mx + b
y = kx
k = xy
What is the equation to find "k", the constant of proportionality?
k = xy
y = kx
y = mx + b
k = yx
The phrase "y varies directly with x" means a relationship is a direct variation.
True
False
If there is no constant of proportionality, k, then the relationship is NOT a direct variation.
True
False
Is the relationship in the table a direct variation?
Yes
No
Is the relationship in the table a direct variation?
Yes
No
Determine if there is a constant of proportionality, k.
If there is a k, what is it?
There is no k
k = 81
k = 8
What is the equation for the given relationship in the table?
y = 8x
y = 81x
y = 8x + 3
y = 81x + 3
Does the graph show a direct variation?
Yes
No
What is the equation for the given graph?
y = 301x
y = 30x
Does the given graph show a direct variation?
Yes
No
What is the equation for the given graph?
y = 601x
y = 60x
Does the given graph show a direct variation?
Yes
No
Suppose y varies directly as x. If x = 27 when y = 6, find x when y = 2.
0.44
81
23
9
The amount a store earns varies directly as the number of hours. A local store takes in $11,500 in a 4 hour period. Estimate how many hours it would take the store to earn $23,000
2 hours
8 hours
11,504 hours
66,125,000 hours
Suppose y varies directly as x. If x = 24 when y = 8, find y when x = 33.
-1
5.8
11
99
The number of apples sold varies directly as the cost. If 4 apples cost $0.45, find the cost of 12 apples.
$1.35
$106.67
$0.45
$0.15
Suppose y varies directly as x. If y = 30 when x = 8, find y when x = 4.
1.07
15
26
60
The size of a box varies directly as its mass. A 20 cubic centimeter box has a mass of 40 kg. What is the size of the box if the mass is 100 kg.
8 cubic centimeters
50 cubic centimeters
80 cubic centimeters
200 cubic centimeters
Suppose y varies directly as x. If y = 150 when x = 3, find y when x = 5.
0.1
90
153
250
On a scale, yards vary directly as feet. If 3 feet represent 30 yards, how many yards represent 5 feet.
0.5 yards
18 yards
32 yards
50 yards
Suppose y varies directly as x. If y = -4 when x = 32, find x when y = -0.375.
0.05
3
27.6
341.3
The number of books sold varies directly as the cost of the books. If 8 books cost $10.40, how many books can be bought for $32.50?
25 books
30 books
32 books
42 books
Suppose y varies directly as x. If x = 15 when y = 12, find x when y = 21.
8.57
16.8
24
26.25
The number of days worked varies directly as the amount earned. If a woman earns $805 for 7 days, how many days does she have to work to earn $1840?
16 days
1042 days
20171 days
211600 days
Suppose y varies directly as x. If y = -7 when x = -14, find x when y = 10.
-5
3
9.8
20
Suppose y varies directly as x. If y = 3 when x = 15, find x when y = 5.
25
17
9
1
In the equation y=kx, k is called the ______.
Independent Variable
Dependent Variable
Constant of Variation
Statement of Variation
" y varies proportionally as x"
This is an example of
Equation of Variation
Variation Statement
Dependent Variable
Independent Variable
Is this a direct variation?
YES
NO
Is this a direct variation?
YES
NO
Is this a direct variation?
YES
NO
What is the constant of variation in the equation, y = 3 (x+z) ?
y
3
x
z
Are all linear equations direct variations?
Yes, because they all linear equations have constant of variations.
Yes, because all linear equations create a straight line.
No, because not all linear equations pass through the origin.
No, because linear equations does not contain any constant of variation.
If y varies directly as x and y = 18 when x = 3, Find y when x = 7.
16
34
42
49
Using the standard formula of direct variation, find x if k=2 and y=4.
8
1/2
4
2
What is the constant of proportionality based on the table if y varies directly as x?
5
3/4
1/3
3
An equation of direct variation can be written in the form: y = kx
True
False
If y varies directly as x and y = 18 when x = 3, Find y when x = 7.
16
34
42
49
The variables y & x vary directly. y=−27 when x = 9
Find the value of y when x=20
-6.67
60
-60
14
40
-40
5
-5
7
-7
-7.2
The letter k in the equation y = kx stands for
the constant of proportionality
king
queen
Is this table proportional or non-proportional?
Yes
No
Identify the constant of proportionality.
k = 2
k = 3
k = 1.50
k = 2/3
none (not proportional)
Craig earns extra money as a lifeguard. He earns $37 for 4 hours and $64.75 for 7 hours. What is the constant of proportionality in dollars per hour?
$37 / hour
$64.75 / hour
$9.25 / hour
$18.50 / hour
What is the constant of proportionality? (Unit rate)
2 swings / 1 day
0.5 swings / 1 day
4 swings / 1 day
None of the above
Find the constant proportionality of 624 calories in 3 servings.
Is the given table a proportional relationship? If so, what is the constant of proportionality?
Identify the constant of proportionality.
k = 2
k = 3
k = 1.50
k = 2/3
none (not proportional)
What is the constant of proportionality?
2 swings / 1 day
0.5 swings / 1 day
4 swings / 1 day
None of the above
Find the constant proportionality of 624 calories in 3 servings.
Craig earns extra money as a lifeguard. He earns $37 for 4 hours and $64.75 for 7 hours. What is the constant of proportionality in dollars per hour?
$37 / hour
$64.75 / hour
$9.25 / hour
$18.50 / hour
Identify the constant of proportionality.
k = 5
k = 1/5
k = 1
k = 2.5
none (not proportional)
Identify the constant of proportionality.
k = 25
k = 50
k = 100
k = 1/50
none (not proportional)
The Williams family bought four concert tickets for $252. What was the price per ticket?
$62.00
$6.30
$63.00
$60.00
What is the constant of proportionality for the table above?
X=4
X=3
X=1/2
No C.O.P
Which tables and graphs show a proportional relationship?
A,B,D
A,C,F
B,D,E
B,C,F
Find the unit rate.
18 orders in 3 days = ________ orders per day
3
9
6
8
A parking lot has 3 cars and 12 trucks. Find the ratio of cars to trucks. Select all the true ratios.
3 trucks : 12 cars.
1 truck : 12 cars
1 truck : 4 car
3 cars : 12 trucks
In the equation y = 14x, what is the constant of proportionality?
x
14
y
You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?
$8 per pound
$35 per pound
$5 per pound
0.125 pounds per dollar
The Williams family bought four concert tickets for $252. What was the price per ticket?
$62.00
$6.30
$63.00
$60.00
What is the ratio of red apples to green apples
4 red apples to 3 green apples
3 green apples to 4 red apples
4 red apples to 7 apples
7 apples to 3 green
What is a Ratio?
It is when the only factor the numerator and denominator share is a one
Is a comparison of two quantities
A rate with a denominator of one
Two decimals that can be multiplied
What is the constant of proportionality for this table?
8
3
1/9
9
The constant of proportionality can be found by finding the __________ _____________.
proportion answer
unit rate
rational number
ratio rate
What is the constant of proportionality?
2
10
5
1/5
Is the given table a proportional relationship? If so, what is the constant of proportionality?
Yes; X=1/3
No
Yes; X=3
Yes; X=5
What is the constant of proportionality for the table above?
X=4
X=3
X=1/2
No C.O.P
Does this graph show a proportional relationship?
Yes
No
What makes a graph proportional?
A straight line (linear) that goes through the origin
Linear (straight line), that does NOT go through the origin.
What is the ordered pair that represents the unit rate?
(2,30)
(1,15)
(15,1)
(6,40)
Does this graph show a proportional relationship?
Sometimes
Yes
No
Which graph shows a proportional relationship?
Which tables and graphs show a proportional relationship?
A,B,D
A,C,F
B,D,E
B,C,F
Albert wants to buy some pens. He compares 4 different packs of pens. Which two packs of pens have the same cost per pen?
Packs 1 and 2
Packs 1 and 4
Packs 1 and 3
Packs 2 and 4
The constant of proportionality in the equation y = ½x is _______.
1/2
x
y
2
Identify the constant of proportionality.
k = 2
k = 3
k = 1.50
k = 2/3
none (not proportional)
What is the constant of proportionality for the table above?
2
3
1/2
None of these
Find the Constant of Proportionality.
(a)
Find the Constant of Proportionality.
(a)
Find the Constant of Proportionality.
(a)
Find the Constant of Proportionality.
(a)
Find the Constant of Proportionality. (Leave as a fraction)
(a)
Write the equation that matches the given proportional relationship.
(a)
What is the EQUATION for this table?
y = 1/2x
x = 1/2y
y = 2x
k = x
What is the EQUATION for this table?
y=1/3x
y=3x
y=5x
Not proportional
Write the equation for the table given.
y = 16x
y=8x
y=12x
not proportional
Write an equation for this relationship.
y = 18x
y = 18.50x
y = 22.50x
y = 22x
Write an equation for this relationship
y=28x
y=35x
y=38x
y=26x
Write an equation for this relationship
y=2x
y=3x
y=1.50x
y=2/3x
none (not proportional)
What is the formula for Constant of Proportionality?
y = k + x
y = k - x
y = kx
x = ky
An online game increases in number of users at a rate of 500 users each day. Which graph represents the relationship between y, the number of users, and x, the number of days?
Cheddar Cheese cost $4.25 per pound. Which equation best represents y, the total cost of x pounds of cheddar cheese?
x = 4.25y
y = 4.25x
y = 4.25 - x
y = 4.25 + x
Caroline's cell phone plan cost $32 per month. Which table shows the sum of the amounts that Caroline will pay for her cell phone plan over the next 4 months?
A dolphin travels through the water at a speed of 25 kilometers per hour. Select two representations that show the distance a dolphin can travel at this rate.
y = x + 25
In 5 hours the dolphin can travel 125 kilometers.
Which of these does NOT represent the distance a car travels when going 55 miles per hour?
y = 55 x
In 3 hours the car will travel a distance of of 160 miles.
The graph represents the linear relationship between the number of books Layla has read and the number of months she has been a member of a book club. Which of these statements is supported by the rate of change of this relationship?
Layla read 2 books in the first 3 months she was a member of the book club.
Layla read 3 books in the first 2 months she was a member of the book club.
Layla read 3 books in the first 4 months she was a member of the book club.
Layla read 4 books in the first 3 months she was a member of the book club.
A rate is...
Is a comparison of two quantities with a common denominator/unit.
a ratio that compares two quantities of different units.
a rate when the second quantity in the comparison ( aka the denominator ) is a unit of one.
two ratios set equal to one another.
A unit rate is...
Is a comparison of two quantities with a common denominator/unit.
a ratio that compares two quantities of different units.
a rate when the second quantity in the comparison ( aka the denominator ) is a unit of one.
two ratios set equal to one another.
A proportion is...
Is a comparison of two quantities with a common denominator/unit.
a ratio that compares two quantities of different units.
a rate when the second quantity in the comparison ( aka the denominator ) is a unit of one.
two ratios set equal to one another.
A worker uses 450 inches of steel wire to make 300 springs the same size. At this rate how many inches of steel wire are needed to make 1 spring?
31in.
15 1in.
32in.
12 1in.
Tareq pays $22.10 for 2.6 pounds of salmon. What is the price per pound of the salmon?
$57.46
$8.50
$19.50
$24. 70
At a school carnival, tickets can be purchased to participate in different activities. The table shows the cost of different numbers of tickets. What is the constant of proportionality that relates y, the total cost in dollars to x, the number of tickets purchased?
$4.00
$0.25
$1.00
$0.10
A recipe says to use 3 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made, y, to the number of cups of flour used in, x?
0.6
48
3
16
Sia saves 25 dollar per month. Miguel's savings are shown in the graph. After two months, how much more would Sia have saved than Miguel?
$10
$20
$30
$40
Based on the graph, what is the slope (rate of change) of a canoe rental?
$6 per hour
$12 per hour
$24 per hour
$1 per 12 hours
Review: What makes this graph not proportional?
does not have a constant unit rate/slope
is not straight line
does not pass through (0,0)
Select all true statements
A is not proportional but B is
both pass through (0,0)
y = 3x is the equation for table A
y = 4x is the equation for table B
if graphed, these tables would make the same line
Which company charges the lowest price per hour to rent a raft?
Water's Edge Rafts
Ryan's Rafts
They charge the same rate per hour
The graph shows the number of headphones produced by Soundtech. NewSounds produces 175 headphones per hour.
Which statement is true?
NewSounds produces headphones at a faster rate.
Soundtech produces headphones at a faster rate.
Both companies produce headphones at the same rate.
Neither company is producing headphones at a constant rate.
Review: Is this proportional?
yes
no
Review: What makes this graph not proportional?
does not have a constant unit rate/slope
is not straight line
does not pass through (0,0)
Select the true statements related to the graph comparison.
neither are proportional
they have different constants of proportionality (k)
graph A is steeper than graph B
the constant of proportionality (k) for both is 4
the constant of proportionality (k) for both is 1/4
Select the true statements.
graph A is not proportional but B is
graph B is less steep than graph A
graph B passes through the origin and A does not
the constant of proportionality of graph B is less than A
both are straight lines
Select all true statements
A is not proportional but B is
both pass through (0,0)
y = 3x is the equation for table A
y = 4x is the equation for table B
if graphed, these tables would make the same line
Does this graph represent this table?
yes
no
Is this equation y = 14x showing proportionality?
yes
no
