A botanist uses the representations below to show the heights in inches, h, of different
plants over a period of time, t.
Plant A
Time in weeks, t
Height in inches, h
60
90
80
120
100
150
120
180
Plant B
If the growth patterns continue, how much taller is the tallest plant than the shortest plant at
120 weeks of growth?
180 inches
200 inches
270 inches
280 inches
The table shows the number of minutes Jalen talks on his mobile phone and the cost of the
phone calls.
Number of
minutes, x
Cost, y
150
Jalen’s Mobile Phone Cost
220
250
275
$7.50
$11.00
$12.50
$13.75
If the cost varies directly with the number of minutes Jalen talks on the phone, which
equation represents the variation?
Which statement correctly compares the constants of variation for the graph and the
equation below?
The graph has a greater constant of variation.
The equation has a greater constant of variation.
The constant of variation is the same for the graph and the equation.
The constant of variation cannot be compared because the equation is nonproportional.
Which explains whether or not the graph represents a direct variation?
The graph has a constant of variation of 3, so it represents a direct variation.
The graph has a slope of 3, so it represents a direct variation.
The graph has a positive slope, so it does not represent a direct variation.
The graph does not begin at the origin, so it does not represent a direct variation.
A painter made the table below to show the amount of paint it takes to cover a certain
amount of square feet. The amount of paint varies directly with the area of each wall.
Area of wall
,x
Amount of paint
(pints), y
Amount of Paint and Size of Wall
64
144
4
9
400
25
How much paint should the painter expect to use to paint a wall with an area of 256 square
feet?
16 pints
32 pints
128 pints
225 pints
Which representation has a constant of variation of –2.5?
–2
–5
x
y
B
C
D
A
B
C
D
A
–3
–7.5
–4
–10
–5
–12.5
Caleb made the table below to show the number of hours he works and the amounts he
earns over a four-week period.
Hours
Earnings
(in dollars)
12
140
Caleb’s Earnings
15
170
18
200
21
230
Which describes whether the relationship between the earnings and the number of hours
represents a direct variation?
He earns 20 more than 10 times the number of hours he works each week, so the earnings
vary directly with the hours.
The earnings increase by 30 for every increase of 3 hours, so the earnings vary directly
with the hours.
The ratios of earnings to hours are not the same each week, so the earnings do not vary
directly with the hours.
The earnings increase at a steady rate, so the earnings do not vary directly with the hours.
Lydia writes the equation below with a missing value.
She puts a value in the box and says that the equation represents a direct variation. Which
explains whether the equation could represent a direct variation?
If she puts 0 in the box she would have a direct variation.X
If she puts 5 in the box she would have a direct variation.
The equation is not of the form
, so it cannot represent a direct variation.
The equation has a minus sign, so it cannot represent a direct variation.
The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly
with the weight of the dog. If the veterinarian gives a 30-pound dog
medicine, which equation relates the weight, w, and the dosage, d?
milligram of the