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

Question 1

Find the slope of the line containing the given points. $P _ { 1 } ( 2,8 ) , \quad P _ { 2 } ( 3,11 )$

A) -3
B) 3
C) $- \frac { 1 } { 3 }$
D) $\frac { 3 } { 5 }$
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 $\pi$ times diameter.

A) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \pi d ^ { 2 }$
B) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \pi d$
C) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \frac { d } { \pi }$
D) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \pi ^ { 2 } d$
E) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \frac { \pi } { d }$

Question 5

Find $g ( - 2 )$ and $g ( 3 )$ . $g ( x ) = 1 - x ^ { 2 }$

A) $5$ , $- 6$
B) $- 3$ , $- 8$
C) $3$ , $- 11$
D) $- 1$ , $- 2$
E) $- 6$ , $4$

Question 6

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) $( - 2,0 ) \text { and } ( 0,5 )$

A) 0
B) $- \frac { 5 } { 2 }$
C) $- 2$
D) $\frac { 5 } { 2 }$
E) undefined

Question 7

Given the function $s ( t ) = \frac { 3 } { 2 t - 1 }$ , find $s ( - 3 )$

A) $- \frac { 3 } { 7 }$
B) $3$
C) $\frac { 3 } { 7 }$
D) $- \frac { 1 } { 7 }$
E) $- \frac { 3 } { 5 }$

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. $P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 )$

A) 4
B) $- \frac { 1 } { 2 }$
C) 0
D) 2
E) $\frac { 1 } { 2 }$

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; $16 A ( x ) = x$
B) A = amount earned ($); x = number of hours worked; $x ( A ) = 16 A$
C) A = amount earned ($); x = number of hours worked; $A ( x ) = \frac { 1 } { 16 } x$
D) A = amount earned ($); x = number of hours worked; $x ( A ) = \frac { 1 } { 16 } A$
E) A = amount earned ($); x = number of hours worked; $A ( x ) = 16 x$

Question 11

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each you use it.) $( - 7 , - 4 ) \text { and } ( - 7,2 )$

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

Question 12

Use the slope formula to find slope. $( 6,0 ) \text { and } ( 9,5 )$

A) $- \frac { 5 } { 3 }$
B) $\frac { 9 } { 5 }$
C) $\frac { 5 } { 3 }$
D) $- \frac { 9 } { 5 }$
E) $5$

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. $P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 )$

A) $\frac { 3 } { 8 }$
B) $\frac { 1 } { 4 }$
C) $- \frac { 3 } { 8 }$
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.) $( - 2,9 ) \text { and } ( 2,9 )$

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

Question 16

Given the function $f ( x ) = - x ^ { 3 } - 10 x - 17$ , find $f ( - 3 )$

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.) $( 3 , - 1 ) \text { and } ( 2 , - 1 )$

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 $g ( - 3 )$ and $g ( 4 )$ . $g ( x ) = x ^ { 2 } + 1$

A) $8$ , $13$
B) $10$ , $17$
C) $6$ , $14$
D) $8$ , $18$
E) $7$ , $17$

Question 21

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

A) $y = 3 x + 5$
B) $y = 3 x - 2$
C) $y = 3 x + 2$
D) $y = 3 x - 5$
E) $y = 3 x - 8$

Question 22

Find the slope and y-intercept of the line $3 x + 4 y = 12$

A) $m = - \frac { 3 } { 4 }$ (0, 5)
B) $m = \frac { 3 } { 4 }$ (5, 0)
C) $m = - \frac { 3 } { 4 }$ (0, 3)
D) $m = - \frac { 3 } { 4 }$ (0, -5)
E) $m = \frac { 3 } { 4 }$ (0, -3)

Question 23

Write an equation for the given data. slope = $\frac { 6 } { 7 } , y \text {-intercept } = - 5$

A) $y = \frac { 6 } { 7 } x + 5$
B) $y = - 5 x + \frac { 6 } { 7 }$
C) $y = 5 x + \frac { 6 } { 7 }$
D) $y = - \frac { 6 } { 7 } x + 5$
E) $y = \frac { 6 } { 7 } x - 5$

Question 24

Arrange slopes from flattest to steepest. $\frac { 7 } { 6 } , \frac { 6 } { 7 } , 1$

A) $\frac { 7 } { 6 } , \frac { 6 } { 7 } , 1$
B) $\frac { 6 } { 7 } , \frac { 7 } { 6 } , 1$
C) $1 , \frac { 7 } { 6 } , \frac { 6 } { 7 }$
D) $\frac { 6 } { 7 } , 1 , \frac { 7 } { 6 }$
E) $\frac { 7 } { 6 } , 1 , \frac { 6 } { 7 }$

Question 25

Find the slope and y-intercept of the line $- 2 x + 3 y = 9$

A) $m = \frac { 2 } { 3 }$ (0, 5)
B) $m = - \frac { 2 } { 3 }$ (5, 0)
C) $m = \frac { 2 } { 3 }$ (0, -3)
D) $m = \frac { 2 } { 3 }$ (0, 3)
E) $m = - \frac { 2 } { 3 }$ (0, -3)

Question 26

Use the slope formula to find the slope. $( a , c )$ and $( b , c )$

A) $\frac { b } { a }$
B) b
C) 0
D) a
E) undefined

Question 27

Find x if f(x) = 0. $f ( x ) = 5 x - 2 ( x - 13 )$

A) $x = 8 \frac { 2 } { 3 }$
B) $x = 7 \frac { 1 } { 3 }$
C) $x = - 7 \frac { 1 } { 3 }$
D) $x = - 8 \frac { 2 } { 3 }$
E) $x = 5 \frac { 1 } { 2 }$

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. $( 4,4 )$ and $( \mathrm { k } , \mathrm { g } )$

A) $\frac { k + 5 } { g + 5 }$
B) $\frac { g - 4 } { k - 4 }$
C) $\frac { k - 4 } { g - 4 }$
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) $y = 4 x - 1$
B) $y = - 3 x + 4$
C) $y = 3 x - 4$
D) $y = - 3 x + 1$
E) $y = - 3 x + 5$

Question 32

Arrange slopes from flattest to steepest. $- \frac { 2 } { 9 } , 0 , - \frac { 9 } { 2 }$

A) $0 , - \frac { 9 } { 2 } , - \frac { 2 } { 9 }$
B) $- \frac { 2 } { 9 } , - \frac { 9 } { 2 } , 0$
C) $- \frac { 2 } { 9 } , 0 , - \frac { 9 } { 2 }$
D) $- \frac { 9 } { 2 } , - \frac { 2 } { 9 } , 0$
E) $0 , - \frac { 2 } { 9 } , - \frac { 9 } { 2 }$

Question 33

Write an equation for the given data. $\text { slope } = \frac { 7 } { 6 } , y \text {-intercept } = 3$

A) $y = \frac { 7 } { 6 } x - 3$
B) $y = \frac { 6 } { 7 } x + 3$
C) $y = 3 x + \frac { 7 } { 6 }$
D) $y = \frac { 7 } { 6 } x + 3$
E) $y = 3 x - \frac { 7 } { 6 }$

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) $y = 1.09 x$
B) $y = x + 0.09$
C) $y = x - 0.09$
D) $y = 0.91 x$
E) $y = 0.09 x - 1$

Question 35

Find the slope and the vertical-axis intercept for the equation. Assume that the output variable is on the left. $D = 385 + 55 t$

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. $( \mathrm { k } , \mathrm { g } )$ and $( k , c )$

A) $\frac { \mathrm { g } } { \mathrm { c } }$
B) $\frac { g } { k }$
C) $\frac { \mathrm { k } } { \mathrm { g } }$
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) $y = 2 x + 3$
B) $y = 3 x + 2$
C) $y = 5 x + 2$
D) $y = 4 ( x - 5 )$
E) $y = 2 x + 5$

Question 38

Find the slope and y-intercept for given equation. $y = - \frac { 1 } { 1 } x$

A) $- 6$ , $( 0 , - 6 )$
B) $- \frac { 1 } { 1 }$ , $( 0,0 )$
C) $6$ , $( 0,0 )$
D) $- 7$ , $( 0,0 )$
E) $- \frac { 7 } { 6 }$ , $( 0,0 )$

Question 39

Find the x- and y-intercepts of the line $y = 2 x + 6$

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. $C = 95 + 0.15 ( d - 100 )$

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. $3 x - 4 y > 12$ to $y < \frac { 3 x } { 4 } - 3$

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) $y = 20 x + 500$
B) $y = 500 x + 20$
C) $y = 0.2 x + 500$
D) $y = - 20 x + 500$
E) $y = 0.02 x + 500$

Question 43

Find the equation of the line that contains the point (-9, -6) and has slope $\frac { 4 } { 9 }$ .

A) $y = \frac { 4 } { 9 } x - 2$
B) $y = - \frac { 4 } { 9 } x - 2$
C) $y = - \frac { 4 } { 9 } x + 2$
D) $y = \frac { 4 } { 9 } x + 2$
E) $y = - \frac { 4 } { 9 } x + 4$

Question 44

Which ordered pair is a solution to the inequality? $$2 x - 3 y > 4$$

A) $( 0,1 )$
B) $( - 2,0 )$
C) $( - 1,0 )$
D) $( 1 , - 1 )$
E) $( - 2,2 )$

Question 45

Which ordered pair is a solution to the inequality? $x - y < 9$

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. $2 y - x \geq 6 \text { to } y \geq \frac { 1 } { 2 } x + 3$

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 $\frac { 1 } { 2 }$

Question 47

Find the equation of the line that contains the point (-27, 13) and has slope $- \frac { 4 } { 9 }$ .

A) $y = \frac { 4 } { 9 } x + 1$
B) $y = - \frac { 4 } { 9 } x + 1$
C) $y = - \frac { 4 } { 9 } x - 4$
D) $y = \frac { 4 } { 9 } x - 4$
E) $y = - \frac { 4 } { 9 } x - 2$

Question 48

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

A) $y = - 5 x - 26$
B) $y = - 5 x - 4$
C) $y = - 5 x + 4$
D) $y = - \frac { 13 } { 3 } x - 5$
E) $y = - \frac { 13 } { 3 } x + 5$

Question 49

Which ordered pair is a solution to the inequality? $$\frac { 1 } { 3 } x + y \geq 1$$

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? $$y - \frac { 1 } { 2 } x \leq 2$$

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? $$y \leq - 4$$

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

Question 52

Write the equation for the problem below using $y = m x + b$ 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) $y = 35 x + 400$
B) $y = - 35 x + 400$
C) $y = - 35 x - 400$
D) $y = 400$
E) $y = 35 x - 400$

Question 53

Four equations are shown. a. $y = - \frac { 1 } { 6 } x + 2$
b. $y = 6 x + 4$
c. $y = - 6 x + 2$
d. $6 x + y = 4$ 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? $$2 x + y \leq 1$$

A) $( 1,2 )$
B) $( - 1,0 )$
C) $( 2,0 )$
D) $( 1,2 )$ .
E) $( 1,0 )$

Question 56

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

A) $y = - \frac { 4 } { 5 } x$
B) $y = - \frac { 5 } { 4 } x$
C) $y = 4 x$
D) $y = \frac { 4 } { 5 } x$
E) $y = \frac { 5 } { 4 } x$

Question 57

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

A) $y = - 2 x + 1$
B) $y = - 2 x + 3$
C) $y = - 2 x - 3$
D) $y = 2 x + 3$
E) $y = - 2 x + 4$

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; $C = 2.30 g + 0.80$
B) steeper; $C = 3.20 g$
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) $y = - \frac { 3 } { 5 } x + 3$
B) $y = - \frac { 5 } { 3 } x - 3$
C) $y = 3 x + 3$
D) $y = - \frac { 3 } { 5 } x - 3$
E) $y = \frac { 5 } { 3 } x + 3$

Question 60

Which ordered pair is a solution to the inequality? $$y \leq - 3$$

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? $$x < 3$$

A) $( 3,5 )$
B) $( 2,4 )$
C) $( 3,4 )$
D) $( 4,4 )$
E) $( 5,5 )$

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) $14 x + 16 y > 2,800$
B) $14 x + 16 y < 2,800$
C) $16 x + 14 y < 2,800$
D) $16 x + 14 y \geq 2,800$
E) $14 x + 16 y \geq 2,800$