Deck 5: Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Question 1

Find the slope of the line containing the given points.

A) -3
B) 3
C)
D)
E) Undefined

Answer 1

3

Question 2

Name the set of inputs (domain) and the set of outputs (range). The capital of the state is a function of the name of the state.

A) {capital}; {name of the state}
B) {name of the state}; {capital}
C) {name of governor}; {capital}
D) {area of state}; {capital}
E) {name of state}; {area of state}

Answer 2

{name of the state}; {capital}

Question 3

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range). a. (7, 9), (7, 11), (7, 13)
b. (7, 9), (9, 11), (11, 13)

A) b is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
B) a is a function. Domain is {7}, range is {9, 11, 13}.
C) a is a function. Domain is {7}, range is {9, 11, 13}.
B is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
D) b is a function. Domain is {7}, range is {9, 11, 13}.
A is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
E) a and b are not functions.

Answer 3

b is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.

Question 4

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is times diameter.

A)
B)
C)
D)
E)

Question 5

Find and .

A) ,
B) ,
C) ,
D) ,
E) ,

Question 6

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.)

A) 0
B)
C)
D)
E) undefined

Question 7

Given the function , find

A)
B)
C)
D)
E)

Question 8

Name the set of inputs (domain) and the set of outputs (range). The cost of a long distance telephone call is a function of how long the parties talk.

A) {distance}; {units of time}
B) {cost of call}; {units of time}
C) {units of time}; {cost of call}
D) {units of time}; {distance}
E) {distance}; {cost of call}

Question 9

Find the slope of the line containing the given points.

A) 4
B)
C) 0
D) 2
E)

Question 10

Define variables and write the sentence in function notation. An hourly worker earns $16 per hour. The amount earned is a function of the number of hours worked.

A) A = amount earned ($); x = number of hours worked;
B) A = amount earned ($); x = number of hours worked;
C) A = amount earned ($); x = number of hours worked;
D) A = amount earned ($); x = number of hours worked;
E) A = amount earned ($); x = number of hours worked;

Question 11

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each you use it.)

A) -4
B) -7
C) 0
D) 2
E) undefined

Question 12

Use the slope formula to find slope.

A)
B)
C)
D)
E)

Question 13

Given the function f(x) = 2x² - 1, find

A) 17
B) 19
C) -13
D) 21
E) 20

Question 14

Find the slope of the line containing the given points.

A)
B)
C)
D) 0
E) undefined

Question 15

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.)

A) 9
B) 0
C) 10
D) 8
E) undefined

Question 16

Given the function , find

A) 74
B) 22
C) 40
D) -20
E) 14

Question 17

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range). a. (9, 99), (9, 999), (9, 9999)
b. (-4, 8), (-5, 8), (-6, 8)

A) a is a function. Domain is {9}, range is {99, 999, 9999}.
B) b is a function. Domain is {-4, -5, -6}, range is {8}.
C) a is a function. Domain is {9}, range is {99, 999, 9999}.
B is a function. Domain is {-4, -5, -6}, range is {8}.
D) b is a function. Domain is {9}, range is {99, 999, 9999}.
A is a function. Domain is {-4, -5, -6}, range is {8}.
E) a and b are not functions.

Question 18

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.)

A) 0
B) 2
C) -1
D) -2
E) -3

Question 19

Is the set of ordered pairs a function? For each function, name the set of inputs (domain) and the set of outputs (range). (Dou, Ron), (Dou, Ian), (Dou, Vernon)

A) Function. Domain is {Dou}, range is {Ron, Ian, Vernon}.
B) Function. Domain is {Dou}, range is {Ron}.
C) Function. Domain is {Dou}, range is {Ron, Ian}.
D) Function. Domain is {Ron, Ian, Vernon}, range is {Dou}.
E) Not a function

Question 20

Find and .

A) ,
B) ,
C) ,
D) ,
E) ,

Question 21

Find the equation of the line that passes through the points (1, -2) and (4, 7).

A)
B)
C)
D)
E)

Question 22

Find the slope and y-intercept of the line

A) (0, 5)
B) (5, 0)
C) (0, 3)
D) (0, -5)
E) (0, -3)

Question 23

Write an equation for the given data. slope =

A)
B)
C)
D)
E)

Question 24

Arrange slopes from flattest to steepest.

A)
B)
C)
D)
E)

Question 25

Find the slope and y-intercept of the line

A) (0, 5)
B) (5, 0)
C) (0, -3)
D) (0, 3)
E) (0, -3)

Question 26

Use the slope formula to find the slope. and

A)
B) b
C) 0
D) a
E) undefined

Question 27

Find x if f(x) = 0.

A)
B)
C)
D)
E)

Question 28

If output values get smaller as input values get larger, then a straight line drawn from the table will :

A) have an undefined slope.
B) have a zero slope.
C) have a positive slope.
D) have a negative slope.
E) fail the vertical-line test.

Question 29

Use the slope formula to find the slope. and

A)
B)
C)
D) 0
E) undefined

Question 30

Find the x- and y-intercepts of the line 2x + 3y = 12 .

A) (4, 0), (0, 6)
B) (-6, 0), (0, 4)
C) (6, 0), (0, 4)
D) (4, 0), (0, -6)
E) (6, 0), (0, -4)

Question 31

Find the equation of the line that passes through the points (0, 1) and (4, -11).

A)
B)
C)
D)
E)

Question 32

Arrange slopes from flattest to steepest.

A)
B)
C)
D)
E)

Question 33

Write an equation for the given data.

A)
B)
C)
D)
E)

Question 34

The output is the total cost of a shirt, where x is the price of the shirt and a sales tax of 9% of the price is added. Write an equation describing the output (y) as a function of the input (x).

A)
B)
C)
D)
E)

Question 35

Find the slope and the vertical-axis intercept for the equation. Assume that the output variable is on the left.

A) The slope is -385 and the vertical-axis intercept is 55.
B) The slope is 385 and the vertical-axis intercept is 55.
C) The slope is 55 and the vertical-axis intercept is 385.
D) The slope is 55 and the vertical-axis intercept is -385.
E) The slope is -55 and the vertical-axis intercept is 385.

Question 36

Use the slope formula to find the slope. and

A)
B)
C)
D) 0
E) undefined

Question 37

The output is the total cost of a taxi ride of x miles. The taxi driver charges a $5 fee plus $2 for each mile traveled. Write an equation describing the output (y) as a function of the input (x).

A)
B)
C)
D)
E)

Question 38

Find the slope and y-intercept for given equation.

A) ,
B) ,
C) ,
D) ,
E) ,

Question 39

Find the x- and y-intercepts of the line

A) (-5, 0), (0, 7)
B) (0, -5), (7, 0)
C) (-3, 0), (0, 6)
D) (-5, 0), (0, -7)
E) (-3, 0), (0, -6)

Question 40

Find the slope and the vertical-axis intercept for the equation. Assume that the output variable is on the left.

A) The slope is 80 and the vertical-axis intercept is 0.15.
B) The slope is 0.15 and the vertical-axis intercept is 95.
C) The slope is 0.25 and the vertical-axis intercept is 95.
D) The slope is 0.15 and the vertical-axis intercept is 80.
E) The slope is 90 and the vertical-axis intercept is 0.15.

Question 41

Identify the steps needed to change the first inequality into the second. to

A) Subtract 3x from both sides.
Divide both sides by -4 and reverse inequality sign.
B) Subtract 3x from both sides.
Divide both sides by 4 and reverse inequality sign.
C) Add 4y to both sides.
Divide both sides by -3 and reverse inequality sign.
D) Add 4y to both sides.
Divide both sides by 3 and reverse inequality sign.
E) Add 4y to both sides.
Divide both sides by 3.

Question 42

Alberto earns a weekly salary of $500 plus 20% of his sales volume. Write an equation describing the total weekly earnings for x dollars in sales.

A)
B)
C)
D)
E)

Question 43

Find the equation of the line that contains the point (-9, -6) and has slope .

A)
B)
C)
D)
E)

Question 44

Which ordered pair is a solution to the inequality?

A)
B)
C)
D)
E)

Question 45

Which ordered pair is a solution to the inequality?

A) (12, 1)
B) (-1, -11)
C) (31, 3)
D) (2, -4)
E) (3, -7)

Question 46

Identify the steps needed to change the first inequality into the second.

A) Subtract x from both sides
Divide both sides by 2
B) Subtract x from both sides
Divide both sides by 2 and reverse the inequality sign
C) Add x to both sides
Divide both sides by 2 and reverse the inequality sign
D) Add x to both sides
Divide both sides by 2
E) Multiply both sides by

Question 47

Find the equation of the line that contains the point (-27, 13) and has slope .

A)
B)
C)
D)
E)

Question 48

Find the equation of the line that contains the point (6, -26) and has slope -5.

A)
B)
C)
D)
E)

Question 49

Which ordered pair is a solution to the inequality?

A) (-3, 1)
B) (3, -1)
C) (6, -1)
D) (-12, 2)
E) (-15, 3)

Question 50

Which ordered pair is a solution to the inequality?

A) (4, 5)
B) (-4, 3)
C) (0, 5)
D) (7, 6)
E) (4, 0)

Question 51

Which ordered pair is a solution to the inequality?

A)
B)
C)
D)
E)

Question 52

Write the equation for the problem below using Yolanda's $400 monthly expense account is set up through an automatic teller machine (ATM). She withdraws funds, using the $35 Fast Cash Option. The equation describes the amount that remains in her account after she makes x withdrawals during the month.

A)
B)
C)
D)
E)

Question 53

Four equations are shown. Which lines are parallel?

A) c and b
B) c and d
C) c and a
D) d and a
E) a and b

Question 54

In the problem below, state whether the described change gives a parallel line or a steeper line and write the new equation. The total monthly cost, in dollars, of a loan is C = 0.01x + 3, where x is the number of dollars borrowed and 3 is the current service fee. The service fee rises by 9 dollars.

A) steeper; C = 9.01x + 3
B) parallel; C = 0.01x + 9
C) steeper; C = 0.01x + 12
D) parallel; C = 9.01x + 3
E) parallel; C = 0.01x + 12

Question 55

Which ordered pair is a solution to the inequality?

A)
B)
C)
D)
E)

Question 56

Find the equation of the line that passes through the points (0, 0) and (-5, 4).

A)
B)
C)
D)
E)

Question 57

Find the equation of the line that contains the point (-1, 3) and has slope -2.

A)
B)
C)
D)
E)

Question 58

In the problem below, state whether the described change gives a parallel line or a steeper line and write the new equation. The total cost, in dollars, of gasoline is C = 2.30g, where g is in gallons. The gasoline rises in price by $0.80 per gallon.

A) parallel;
B) steeper;
C) parallel; C = 3.20g + 0.80
D) steeper; C = 3.10g
E) parallel; C = 3.10g

Question 59

Find the equation of the line that passes through the points (0, 3) and (-5, 6).

A)
B)
C)
D)
E)

Question 60

Which ordered pair is a solution to the inequality?

A) (-2, -2)
B) (3, 5)
C) (5, -3)
D) (-4, 4)
E) (-1, 0)

Question 61

A dieter limits a snack to 75 calories. What are three possible combinations of small carrots at 25 calories each and medium celery stalks at 3 calories each.

A) The first combination: 1 carrot and 19 celery stalks.
The second combination: 2 carrots and 8 celery stalks.
The third combination: 3 carrots and 0 celery stalks.
B) The first combination: 1 carrot and 16 celery stalks.
The second combination: 2 carrots and 10 celery stalks.
The third combination: 3 carrots and 0 celery stalks.
C) The first combination: 1 carrot and 16 celery stalks.
The second combination: 2 carrots and 8 celery stalks.
The third combination: 3 carrots and 2 celery stalks.
D) The first combination: 1 carrot and 19 celery stalks.
The second combination: 2 carrots and 10 celery stalks.
The third combination: 3 carrots and 2 celery stalks.
E) The first combination: 1 carrot and 16 celery stalks.
The second combination: 2 carrots and 8 celery stalks.
The third combination: 3 carrots and 0 celery stalks.

Question 62

Which ordered pair is a solution to the inequality?

A)
B)
C)
D)
E)

Question 63

To meet expenses, a local theater group has a ticket sales goal of $2800. Regular tickets sell for $16 and student/senior tickets sell for $14. Let x = number of regular tickets sold and y = number of student/senior tickets sold. Write an inequality describing possible combinations of ticket sales that would meet, or surpass, the goal.

A)
B)
C)
D)
E)