Deck 1: Linear Equations and Graphs

Question 1

Solve the problem. Express your answer as an integer or simplified fraction:

-

A)
B)
C)
D)

Answer 1

Question 2

Solve the problem. Express your answer as an integer or simplified fraction:

-7x - (5x - 1) = 2

A)
B) -
C) -
D)

Answer 2

Question 3

Solve the problem. Express your answer as an integer or simplified fraction:

-

A) - 2
B) - 6
C) 14
D) - 14

Answer 3

- 6

Question 4

Solve the problem. Express your answer as an integer or simplified fraction:

--2( 2x + 5) - 4 = -2(x + 2) + 4x

A)
B)
C)
D)

Question 5

Solve the problem. Express your answer as an integer or simplified fraction:

-

A) -
B)
C) -
D)

Question 6

Solve the problem. Express your answer as an integer or simplified fraction:

-

A) - 16
B) - 17
C) - 22
D) - 11

Question 7

Solve:

A) 3
B) - 2
C) 2
D) - 3

Question 8

Solve the inequality and graph. Express your answer in interval notation:

-4x - 4 > 3x - 1

A) (- $\infty$ , 3]
B) (3, $\infty$ )
C) ( -5, $\infty$ )
D) [3, $\infty$ )

Question 9

Solve the inequality and graph. Express your answer in interval notation:

--3( 3x - 2) < -12x - 21

A) [ -9, $\infty$ )
B) ( -9, $\infty$ )
C) (- $\infty$ -9)
D) (- $\infty$ , -9]

Question 10

Solve the inequality and graph. Express your answer in interval notation:

-24x + 8 > 4( 5x + 7)

A) [ 5, $\infty$ )
B) ( 5, $\infty$ )
C) (- $\infty$ , 5]
D) (- $\infty$ , 5)

Question 11

Solve the inequality and graph. Express your answer in interval notation:

--4( -2 - x) < 6x + 19 - 11 - 2x

A) $\phi$
B) (- $\infty$ , $\infty$ )
C) (- $\infty$ , 0)
D) (- $\infty$ , 8)

Question 12

Solve the inequality and graph. Express your answer in interval notation:

--29 $\le$ -4x - 1 $\le$ -13

A) ( 3, 7)
B) [ -7, -3]
C) ( -7, -3)
D) [ 3, 7]

Question 13

Solve the formula for the specified variable:

-S = 2 $\pi$ rh + 2 $\pi$ r² for h

A) h = S - r
B)
C)
D) h = 2 $\pi$ (S - r)

Question 14

Solve the formula for the specified variable:

-7x + 10y = 19 for y

A) - 7x - 10y = -19
B)
C)
D) y = 7x - 19

Question 15

Solve the formula for the specified variable:

-

A)
B)
C)
D)

Question 16

Solve the formula for the specified variable:

-Solve:

A)
B)
C)
D)

Question 17

Find the Celsius temperature (to the nearest degree) when Fahrenheit temperature is 50° by solving the equation 50 = C + 32, where F is the Fahrenheit temperature (in degrees) and C is the Celsius temperature.

A) 96°C
B) 24°C
C) 122°C
D) 10°C

Question 18

Assume that the price per unit d of a certain item to the consumer is given by the equation where x is the number of units in demand. The price per unit from the supplier is given by the equation where x is the number of units supplied. Find the equilibrium price and the equilibrium quantity.

A) equilibrium price: $50 per unit; equilibrium quantity: 30 units
B) equilibrium price: $30 per unit; equilibrium quantity: 50 units
C) equilibrium price: $20 per unit; equilibrium quantity: 50 units
D) equilibrium price: $35 per unit; equilibrium quantity: 50 units

Question 19

A piece of equipment was purchased by a company for $10,000 and is assumed to have a salvage value of $3,000 in 10 years. If its value is depreciated linearly from $10,000 to $3,000, find a linear equation in the form V = mt + b, t time in years, that will give the salvage value at any time t,

A) V = 700t + 10,000
B) V = - 700t - 10,000
C) T = - 700V + 10,000
D) V = - 700t + 10,000

Question 20

Determine whether the slope of the line is positive, negative, zero, or undefined:

-

A) positive
B) zero
C) negative
D) undefined

Question 21

Determine whether the slope of the line is positive, negative, zero, or undefined:

-

A) zero
B) undefined
C) negative
D) positive

Question 22

Determine whether the slope of the line is positive, negative, zero, or undefined:

-

A) positive
B) negative
C) zero
D) undefined

Question 23

Determine whether the slope of the line is positive, negative, zero, or undefined:

-

A) negative
B) zero
C) undefined
D) positive

Question 24

Graph the linear equation and determine its slope, if it exists:

-3x + 5y = 11

A)
B)
C)
D)

Question 25

Graph the linear equation and determine its slope, if it exists:

-2x - 5y = 20

A)
B)
C)
D)

Question 26

Find the slope and y intercept of the graph of the equation:

-y = 2x - 6

A) Slope = 2, y intercept = 6
B) Slope = -6, y intercept = 2
C) Slope = 6, y intercept = 2
D) Slope = 2, y intercept = -6

Question 27

Find the slope and y intercept of the graph of the equation:

-

A)
B)
C)
D)

Question 28

Find the slope and y intercept of the graph of the equation:

-

A)
B)
C)
D)

Question 29

Find the slope and y intercept of the graph of the equation:

-

A)
B)
C)
D)

Question 30

Find the slope and y intercept of the graph of the equation:

-y = x + 3

A) Slope = 3; y intercept = 1
B) Slope = 1; y intercept = 3
C) Slope = 0; y intercept = -3
D) Slope = 3; y intercept = -1

Question 31

Write an equation of the line with the indicated slope and y intercept:

-Slope = 2, y intercept = -4

A) y = 2x - 4
B) y = 4x + 2
C) y = -2x - 4
D) y = 4x - 2

Question 32

Write an equation of the line with the indicated slope and y intercept:

-Slope = -3, y intercept = 5

A) y = 5x - 3
B) y = 3x + 5
C) y = -3x - 5
D) y = -3x + 5

Question 33

Write an equation of the line with the indicated slope and y intercept:

-

A)
B)
C)
D)

Question 34

Write an equation of the line with the indicated slope and y intercept:

-

A)
B)
C)
D)

Question 35

Write an equation of the line with the indicated slope and y intercept:

-

A)
B)
C)
D)

Question 36

Write an equation of the line with the indicated slope and y intercept:

-Slope = 1; y intercept = -5

A) y = -5x + 1
B) y = -x - 5
C) y = x - 5
D) y = -5x - 1

Question 37

Use the graph to find the slope-intercept form of the equation of the line.

A) y = x + 3
B) y = -x + 3
C) y = x - 3
D) y = 3x

Question 38

Write the equation of the line in the following graph.

A) f(x) = -x + 1
B) f(x) =x + 1
C) f(x) =x - 1
D) f(x) = -x - 1

Question 39

Find the slope of the line 3x + 4y = 11.

A)
B) -
C) 0
D) -

Question 40

Use the graph to find the slope, x-intercept and y-intercept of the line.

A)
B)
C)
D)

Question 41

Graph the linear function defined by f(x) = x + 2 and indicate the slope and intercepts.

A)
B)
C)
D)

Question 42

Graph the equation:

-42 + 6y = 0

A)
B)
C)
D)

Question 43

Find the standard form of the equation of the line with slope of - and passing through (4, 4).

A) 2x + 7y = - 36
B) 2x + 7y = 36
C) 7x + 2y = - 36
D) 2x - 7y = 36

Question 44

Find the slope of the line containing the given points:

-( 5, -3); ( -8, 2)

A) -
B)
C) -
D)

Question 45

Find the slope of the line containing the given points:

-(-5, 2) and (0, 2)

A) 0
B)
C) -
D) Undefined

Question 46

Write the equation of a line that passes through (3, 9) and (0, -7). Write the final answer in the form where A, B, and C are integers with no common divisors (other than ±1) and

A) 16x - 3y = -21
B) 16x - 3y = 21
C) -16x + 3y = 21
D) 3x - 16y = 21

Question 47

Write the equation of a line that passes through (-1, 4) and (5, -1). Write the final answer in the form where A, B, and C are integers with no common divisors (other than ±1) and

A) 5x + 6y = -19
B) 5x - 6y = 19
C) 5x + 6y = 19
D) -5x + 6y = 19

Question 48

A small company that makes hand-sewn leather shoes has fixed costs of $320 a day, and total costs of $1200 per day at an output of 20 pairs of shoes per day. Assume that total cost C is linearly related to output x. Find an equation of the line relating output to cost. Write the final answer in the form

A) C = 44x + 320
B) C = 60x + 320
C) C = 44x + 1520
D) C = 60x + 1520

Question 49

The mathematical model represents the cost in dollars a company has in manufacturing x items during a month. Using this model, how much does it cost to produce 600 items?

A) $50.00
B) $0.08
C) $390,000
D) $360,000

Question 50

Use the graph to find the average rate of change:

-

A) 2
B) -
C) - 2
D)

Question 51

Use the graph to find the average rate of change:

-

A) 1
B) -4
C) -1
D) 4

Question 52

Given two points ( , ) and ( , ), the ratio of the change in y to the change in x is called.

A) x-intercept
B) slope
C) equilibrium point
D) break-even point

Question 53

Use the REGRESSION feature on a graphing calculator:

-The paired data below consists of the temperature on randomly chosen days and the amount of a certain kind of plant grew (in millimeters).

Find the linear function that predicts a plant's growth as a function of the temperature. Round your answer to two decimal places.

A)
B) y = 14..57x + 0.21
C) y = 0.21x + 14.57
D)

Question 54

Use the REGRESSION feature on a graphing calculator:

-The use of bottled water in the United States has shown a steady increase in recent years. The table shows the annual per capita consumption for the years 1995 - 2001.

With x being the years since 1995, find the linear function that represents this data. Round your answer to two decimal places.

A) y = 0.89x + 4.07
B)
C) y = 4.07x + 0.89
D)

Question 55

Use the REGRESSION feature on a graphing calculator:

-A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below.

Use linear regression to find a linear function that predicts a student's course grade as a function of the number of hours spent in lab.

A) y = 0.930 + 44.3x
B) y = 44.3 + 0.930x
C) y = 88.6 - 1.86x
D) y = 1.86 + 88.6x

Question 56

Use the REGRESSION feature on a graphing calculator:

-In the table below, x represents the number of years since 2000 and y represents sales (in thousands of dollars) of a clothing company. Use the regression equation to estimate sales in the year 2006. Round to the nearest thousand dollars.

A) $8,000
B) $20,000
C) $14,000
D) $2,000

Question 57

Use the REGRESSION feature on a graphing calculator:

-For some reason the quality of production decreased as the year progressed at a flash drive manufacturing plant. The following data represent the percentage of defective flash drives produced at the plant in the corresponding month of the year.

Use the regression equation with values rounded to four decimals to predict the percentage of defective drives in month 6, June.

A) 2.20%
B) 2.3%
C) 2.15%
D) 2.0%

Question 58

Use the REGRESSION feature on a graphing calculator:

-Efficiency experts rate employees according to job performance and attitude. The results for several randomly selected employees are given below.

Find the regression line which can be used to predict performance rating if attitude rating is known.

A) y = 11.7 + 1.02x
B) y = 92.3 - 0.669x
C) y = 2.81 + 1.35x
D) y = -47.3 + 2.02x

Question 59

Suppose the sales of a particular brand of MP3 player satisfy the relationship , where S represents the number of sales in year x, with corresponding to 2002 . Find the number of sales in 2005.

A) 12,600
B) 6400
C) 4400
D) 4200