3A Worksheet 3A
Short Answer
Find an equation for the line:
5
1. through (2, 6) and perpendicular to y =  x + 1.
4
2. through (–7, –4) and vertical.
Determine whether y varies directly with x. If so, find the constant of variation k and write the
equation.
3.
x
y
6
7.2
11
13.2
16
19.2
21
25.2
4. A cannery processed 605 pounds of strawberries in 3.5 hours. The cannery processed 2100 pounds in 10
hours.
a. Write a linear equation to model the weight of strawberries S processed in T hours.
b. How many pounds of strawberries can be processed in 12 hours?
5. The distance traveled at a constant speed is directly proportional to the time of travel. If Olivia traveled 112
miles in 3.5 hours, how many miles will Olivia travel in 8.9 hours at the same constant speed?
6. Make a mapping diagram for the relation.
{(–1, –3), (0, 1), (3, –1), (4, –6)}
7. Graph the set of data. Decide whether a linear model is reasonable. If so, draw a trend line and write its
equation.
{(1, 7), (–2, 1), (3, 13), (–4, –3), (0, 5)}
Write in standard form an equation of the line passing through the given point with the given slope.
8. slope = –8; (–2, –2)
Determine whether y varies directly with x. If so, find the constant of variation k.
9. 8y = 7x – 27
Find the value of y for a given value of x, if y varies directly with x.
10. If y = 4.8 when x = 2.4, what is y when x = 2.05?
11. If y = 166 when x = 83, what is y when x = 23?
12. A leaky valve on the water meter overcharges the residents for one gallon of water in every
months. The
overcharged amount w varies directly with time t.
a. Find the equation that models this direct variation.
b. How many months it will take for the residents to be overcharged for 8 gallons of water?
Find the slope of the line.
13.
14.
15. A new candle is 8 inches tall and burns at a rate of 2 inches per hour.
a. Write an equation that models the height h after t hours.
b. Sketch the graph of the equation.
16. For
,
.
17. Suppose
Find the value of
18. Graph the equation
and
.
.
.
19. The range of a car is the distance R in miles that a car can travel on a full tank of gas. The range varies
directly with the capacity of the gas tank C in gallons.
a. Find the constant of variation for a car whose range is 341 mi with a gas tank that holds
22 gal.
b. Write an equation to model the relationship between the range and the capacity of the
gas tank.
Find the slope of the line through the pair of points.
1
1 1
20. ( , 0) and ( ,  )
3
2 2
3A Worksheet 3A
Answer Section
SHORT ANSWER
1. ANS:
4
22
y= x 
5
5
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 7
2. ANS:
x = –7
REF: 2-2 Linear Equations
STA: ID AL.01.a | ID AL.03.a | ID F.01.a
KEY: slope | perpendicular | equation of a line
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 7
3. ANS:
yes; k = 1.2; y = 1.2x
REF: 2-2 Linear Equations
STA: ID AL.01.a | ID AL.03.a | ID F.01.a
KEY: vertical line | horizontal line | equation of a line
PTS: 1
DIF: L3
REF: 2-3 Direct Variation
OBJ: 2-3.1 Writing and Interpreting a Direct Variation
STA: ID M.03.a | ID F.02.a | ID PS.03 | ID PS.04
TOP: 2-3 Example 1
KEY: constant of variation | direct variation
4. ANS:
S = 230T – 200; 2560 lb
PTS: 1
DIF: L2
REF: 2-4 Using Linear Models
OBJ: 2-4.2 Predicting With Linear Models
STA: ID AL.01.a | ID PS.03 | ID PS.04
TOP: 2-4 Example 2
KEY: linear equation | word problem | problem solving | multi-part question
5. ANS:
284.8 mi
PTS:
OBJ:
STA:
KEY:
6. ANS:
1
DIF: L2
REF: 2-3 Direct Variation
2-3.1 Writing and Interpreting a Direct Variation
ID M.03.a | ID F.02.a | ID PS.03 | ID PS.04
TOP: 2-3 Example 4
direct variation | proportion | problem solving | word problem
–1
–3
0
1
3
–1
4
–6
PTS: 1
DIF: L2
OBJ: 2-1.1 Graphing Relations
TOP: 2-1 Example 3
7. ANS:
REF: 2-1 Relations and Functions
STA: ID F.01 | ID F.02
KEY: relation | mapping diagram | ordered pair
yes;
y
12
8
4
–4
O
4
8
12
x
–4
PTS: 1
DIF: L3
REF: 2-4 Using Linear Models
OBJ: 2-4.2 Predicting With Linear Models
STA: ID AL.01.a | ID PS.03 | ID PS.04
TOP: 2-4 Example 4
KEY: linear model | trend line
8. ANS:
8x + y = –18
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 4
9. ANS:
no
PTS:
OBJ:
STA:
KEY:
REF: 2-2 Linear Equations
STA: ID AL.01.a | ID AL.03.a | ID F.01.a
KEY: point-slope form | standard form of linear equation
1
DIF: L2
REF: 2-3 Direct Variation
2-3.1 Writing and Interpreting a Direct Variation
ID M.03.a | ID F.02.a | ID PS.03 | ID PS.04
TOP: 2-3 Example 2
constant of variation
10. ANS:
4.1
PTS:
OBJ:
STA:
KEY:
11. ANS:
46
1
DIF: L2
REF: 2-3 Direct Variation
2-3.1 Writing and Interpreting a Direct Variation
ID M.03.a | ID F.02.a | ID PS.03 | ID PS.04
TOP: 2-3 Example 4
direct variation
PTS:
OBJ:
STA:
KEY:
12. ANS:
1
DIF: L2
REF: 2-3 Direct Variation
2-3.1 Writing and Interpreting a Direct Variation
ID M.03.a | ID F.02.a | ID PS.03 | ID PS.04
TOP: 2-3 Example 4
direct variation
; 20 months
PTS:
OBJ:
STA:
KEY:
13. ANS:
3

5
1
DIF: L3
REF: 2-3 Direct Variation
2-3.1 Writing and Interpreting a Direct Variation
ID M.03.a | ID F.02.a | ID PS.03 | ID PS.04
TOP: 2-3 Example 3
constant of variation | direct variation | multi-part question | problem solving | word problem
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 6
14. ANS:
1

2
REF: 2-2 Linear Equations
STA: ID AL.01.a | ID AL.03.a | ID F.01.a
KEY: point-slope form | standard form of linear equation | slope
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 6
15. ANS:
REF: 2-2 Linear Equations
STA: ID AL.01.a | ID AL.03.a | ID F.01.a
KEY: slope
t
15
10
5
0
5
10
15 h
PTS: 1
DIF: L2
OBJ: 2-4.1 Modeling Real-World Data
TOP: 2-4 Example 1
16. ANS:
–19
REF: 2-4 Using Linear Models
STA: ID AL.01.a | ID PS.03 | ID PS.04
KEY: linear equation | multi-part question
PTS: 1
DIF: L2
OBJ: 2-1.2 Identifying Functions
TOP: 2-1 Example 6
17. ANS:
4
2
7
REF: 2-1 Relations and Functions
STA: ID F.01 | ID F.02
KEY: function notation
PTS: 1
DIF: L3
OBJ: 2-1.2 Identifying Functions
TOP: 2-1 Example 6
18. ANS:
REF: 2-1 Relations and Functions
STA: ID F.01 | ID F.02
KEY: function notation
y
4
2
–4
–2
O
2
4
x
–2
–4
PTS: 1
DIF: L2
OBJ: 2-2.1 Graphing Linear Equations
TOP: 2-2 Example 1
REF: 2-2 Linear Equations
STA: ID AL.01.a | ID AL.03.a | ID F.01.a
KEY: linear equation | graphing
19. ANS:
1
1
15 mi/gal; R = 15 C
2
2
PTS:
OBJ:
STA:
KEY:
20. ANS:
3
1
DIF: L2
REF: 2-3 Direct Variation
2-3.1 Writing and Interpreting a Direct Variation
ID M.03.a | ID F.02.a | ID PS.03 | ID PS.04
TOP: 2-3 Example 3
constant of variation | direct variation | multi-part question | word problem | problem solving
PTS: 1
DIF: L3
OBJ: 2-2.1 Graphing Linear Equations
TOP: 2-2 Example 3
REF: 2-2 Linear Equations
STA: ID AL.01.a | ID AL.03.a | ID F.01.a
KEY: slope