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  ```SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  q(x) can be written in the form f (x) = mx + b.
  So the function is linear.
  2-2 Linear Relations and Functions
  State whether each function is a linear function.
  Write yes or no. Explain.
  1. 5. RECREATION You want to make sure that you
  have enough music for a car trip. If each CD is an
  average of 45 minutes long, the linear function m(x) =
  0.75x could be used to find out how many CDs you
  need to bring.
  SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  a. If you have 4 CDs, how many hours of music is
  that?
  b. If the trip you are taking is 6 hours, how many
  CDs should you bring?
  is linear as it can be The function
  written as
  SOLUTION: a. m(x) = 0.75x
  Replace x with 4.
  m (4) = 0.75(4) = 3
  Therefore, 4 CDs have 3 hours of music.
  b. Replace m with 6.
  6 = 0.75x
  This implies:
  .
  2. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  cannot be written in the form f (x) = mx
  + b.
  So the function is not linear.
  The number of CDs needed for a 6 hour trip is 8.
  3. CCSS STRUCTURE Write each equation in
  standard form. Identify A, B, and C.
  SOLUTION: is not a linear function as x has an
  exponent that is not 1.
  6. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  4. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  q(x) can be written in the form f (x) = mx + b.
  So the function is linear.
  5. RECREATION You want to make sure that you
  have enough music for a car trip. If each CD is an
  average of 45 minutes long, the linear function m(x) =
  0.75x could be used to find out how many CDs you
  need to bring.
  a. If you have 4 CDs, how many hours of music is
  that?
  b. If the trip you are taking is 6 hours, how many
  CDs should you bring?
  SOLUTION: a. m(x) = 0.75x
  A = 4, B = 1, and C = –7.
  7. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are notPage
  both1
  zero.
  A = 4, B = 1, and C = –7.
  2-2 Linear
  Relations and Functions
  7. A = 8, B = 9, and C = 6.
  10. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  A = 6, B = –1, and C = –5.
  A = 1, B = –3, and C = –2.
  8. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  11. SOLUTION: The standard form of a linear equation is Ax + By =
  C,
  where A, B, and C are integers with a greatest
  common factor
  of 1,
  , and A and B are not both zero.
  A = 3, B = 2, and C = –1.
  A = 2, B = –3, and C = 12.
  9. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  A = 8, B = 9, and C = 6.
  10. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where
  B, and by
  C Cognero
  are integers with a greatest
  eSolutions
  ManualA,
  - Powered
  common factor of 1,
  , and A and B are not both
  zero.
  Find the x-intercept and the y-intercept of the
  graph of each equation. Then graph the
  equation using the intercepts.
  12. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  Substitute y = 0 in the equation.
  0 = 5x + 12
  The x-intercept is
  .
  The y-intercept is the value of y when x = 0.
  Page 2
  A = 2, BRelations
  = –3, and and
  C = 12.
  2-2 Linear
  Functions
  Find the x-intercept and the y-intercept of the
  graph of each equation. Then graph the
  equation using the intercepts.
  13. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  12. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  Substitute y = 0 in the equation.
  0 = 5x + 12
  The x-intercept is
  So, the x-intercept is
  .
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is –10.
  .
  The y-intercept is the value of y when x = 0.
  Therefore, the y-intercept is 12
  .
  14. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is 6.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is 4.
  13. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is
  .
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is –10.
  15. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Page 3
  SOLUTION: In a linear function, the exponent of the independent
  variable is less than or equal to 1.
  No; x has an exponent other than 1.
  2-2 Linear Relations and Functions
  15. 18. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is 7.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is
  SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  Yes; it can be written in f (x) = mx + b form, where
  m = 0 and b = 6.
  19. SOLUTION: In a linear function, the exponent of the independent
  variable is less than or equal to 1.
  No; x has an exponent other than 1.
  .
  20. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  No; it cannot be written in f (x) = mx + b form.
  State whether each equation or function is a
  linear function. Write yes or no. Explain.
  21. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  No; it cannot be written in f (x) = mx + b form.
  16. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  Yes; it can be written in f (x) = mx + b form, where
  and 22. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  No; it cannot be written in f (x) = mx + b form.
  .
  17. SOLUTION: In a linear function, the exponent of the independent
  variable is less than or equal to 1.
  No; x has an exponent other than 1.
  23. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  No; it cannot be written in f (x) = mx + b form; There
  is an xy term.
  18. SOLUTION: A linear function is a function with ordered pairs that
  satisfy
  a linear
  equation
  of the form y = mx + b.
  eSolutions
  Manual
  - Powered
  by Cognero
  Yes; it can be written in f (x) = mx + b form, where
  m = 0 and b = 6.
  Page 4
  24. The roller coaster travels 260 meters in 25 seconds.
  b. Kingda Ka; Sample answer: The Kingda Ka
  travels 847.5 meters in 25 seconds, so it travels a
  greater distance in the same amount of time.
  satisfy a linear equation of the form y = mx + b.
  No; it cannot be written in f (x) = mx + b form; There
  2-2 Linear
  and Functions
  is an xyRelations
  term.
  Write each equation in standard form. Identify
  A, B, and C.
  24. SOLUTION: A linear function is a function with ordered pairs that
  satisfy a linear equation of the form y = mx + b.
  Yes; it can be written in f (x) = mx + b form, where
  and 26. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  .
  25. ROLLER COASTERS The speed of the Steel
  Dragon 2000 roller coaster in Mie Prefecture, Japan,
  can be modeled by y = 10.4x, where y is the distance
  traveled in meters in x seconds.
  A = 7, B = 5, and C = –35.
  a. How far does the coaster travel in 25 seconds?
  27. b. The speed of Kingda Ka in Jackson, New Jersey,
  can be described by y = 33.9x. Which coaster travels
  SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  SOLUTION: a. y = 10.4x
  Replace x with 25.
  A = 8, B = 3, and C = –6.
  The roller coaster travels 260 meters in 25 seconds.
  b. Kingda Ka; Sample answer: The Kingda Ka
  travels 847.5 meters in 25 seconds, so it travels a
  greater distance in the same amount of time.
  28. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  Write each equation in standard form. Identify
  A, B, and C.
  26. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  A = 7,
  B = -5,Powered
  and C by
  = Cognero
  –35.
  eSolutions
  Manual
  A = 3, B = –10, and C = –5.
  29. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  Page 5
  27. 2-2 Linear
  Relations and Functions
  A = 3, B = –10, and C = –5.
  29. A = 6, B = 1, and C = 0.
  32. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  A= 2, B = 1, and C = –11.
  30. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  A = 9, B = –8, and C = 2.
  33. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  A = 3, B = –1, and C = 4.
  31. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  A = 5, B = 32, and C = 160.
  34. A = 6, B = 1, and C = 0.
  32. SOLUTION: The standard form of a linear equation is Ax + By =
  eSolutions
  ManualA,
  - Powered
  C, where
  B, and by
  C Cognero
  are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  Page 6
  2-2 Linear
  Relations and Functions
  A = 5, B = 32, and C = 160.
  34. 36. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is 6.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is –18.
  A = 2, B = 31, and C = 78.
  Find the x-intercept and the y-intercept of the
  graph of each equation. Then graph the
  equation using the intercepts.
  35. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is –0.5.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is –4.
  37. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is –7.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is 10.5.
  36. SOLUTION: eSolutions
  The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Page 7
  2-2 Linear Relations and Functions
  37. 38. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is –7.
  So, the x-intercept is
  .
  The y-intercept is the value of y when x = 0.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is 10.5.
  So, the y-intercept is
  .
  38. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is
  .
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is
  .
  39. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y -intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is 12.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is –18.
  Page 8
  2-2 Linear Relations and Functions
  39. 40. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y -intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is 12.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is –18.
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is –18.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is 16.
  40. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The equation is
  .
  The x-intercept is the value of x when y = 0.
  So, the x-intercept is –18.
  The y-intercept is the value of y when x = 0.
  So, the y-intercept is 16.
  41. CCSS MODELING Latonya earns a commission
  of \$1.75 for each magazine subscription she sells and
  \$1.50 for each newspaper subscription she sells. Her
  goal is to earn a total of \$525 in commissions in the
  next two weeks.
  a. Write an equation that is a model for the different
  numbers of magazine and newspaper subscriptions
  that can be sold to meet the goal.
  b. Graph the equation. Does this equation represent a
  function? Explain.
  c. If Latonya sells 100 magazine subscriptions and
  200 newspaper subscriptions, will she meet her goal?
  Explain.
  SOLUTION: a. Let m and n represent the number of magazines
  and newspapers respectively.
  Commission for m magazines = 1.75m
  Page 9
  Commission for n newspapers = 1.5n
  The goal is \$525.
  So:
  2-2 Linear Relations and Functions
  41. CCSS MODELING Latonya earns a commission
  of \$1.75 for each magazine subscription she sells and
  \$1.50 for each newspaper subscription she sells. Her
  goal is to earn a total of \$525 in commissions in the
  next two weeks.
  a. Write an equation that is a model for the different
  numbers of magazine and newspaper subscriptions
  that can be sold to meet the goal.
  b. Graph the equation. Does this equation represent a
  function? Explain.
  c. If Latonya sells 100 magazine subscriptions and
  200 newspaper subscriptions, will she meet her goal?
  Explain.
  SOLUTION: a. Let m and n represent the number of magazines
  and newspapers respectively.
  Commission for m magazines = 1.75m
  Commission for n newspapers = 1.5n
  The goal is \$525.
  So:
  The amount that Latonya will earn is \$475. So, she
  could not meet her goal.
  42. SNAKES Suppose the body length L in inches of a
  baby snake is given by L(m) = 1.5 + 2m, where m is
  the age of the snake in months until it becomes 12
  months old.
  a. Find the length of an 8-month-old snake.
  b. Find the snake’s age if the length of the snake is
  25.5 inches.
  SOLUTION: a.
  L(m) = 1.5 + 2m
  Replace m with 8.
  The length of an 8-month-old snake is 17.5 inches.
  b. Replace L with 25.5 inches.
  b.
  Therefore, the snake is 12 months.
  The graph passes the vertical line test. So, the
  equation represents a function.
  c. Replace m with 100 and n with 200.
  The amount that Latonya will earn is \$475. So, she
  could not meet her goal.
  42. SNAKES Suppose the body length L in inches of a
  baby snake is given by L(m) = 1.5 + 2m, where m is
  the age of the snake in months until it becomes 12
  months
  eSolutions
  Manual
  a. Find the length of an 8-month-old snake.
  43. STATE FAIR The Ohio State Fair charges \$8 for
  admission and \$5 for parking. After Joey pays for
  admission and parking, he plans to spend all of his
  remaining money at the ring game, which costs \$3
  per game.
  a. Write an equation representing the situation.
  b. How much did Joey spend at the fair if he paid \$6
  for food and drinks and played the ring game 4
  times?
  SOLUTION: a. Let x be the number of games that Joey plays.
  The amount spend by Joey is given by:
  b. The amount that Joey spent on admission, parking,
  and food is \$19.
  The amount spent on 4 games = 3(4) = \$12.
  Page 10
  So, the total amount = \$19 + \$12 = \$31.
  Write each equation in standard form. Identify
  2-2 Linear
  Relations and Functions
  Therefore, the snake is 12 months.
  43. STATE FAIR The Ohio State Fair charges \$8 for
  admission and \$5 for parking. After Joey pays for
  admission and parking, he plans to spend all of his
  remaining money at the ring game, which costs \$3
  per game.
  a. Write an equation representing the situation.
  b. How much did Joey spend at the fair if he paid \$6
  for food and drinks and played the ring game 4
  times?
  A = 1, B = 6, and C = 7.
  45. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  SOLUTION: a. Let x be the number of games that Joey plays.
  The amount spend by Joey is given by:
  A = 4, B = –40 , and C = –59.
  b. The amount that Joey spent on admission, parking,
  and food is \$19.
  The amount spent on 4 games = 3(4) = \$12.
  So, the total amount = \$19 + \$12 = \$31.
  46. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  Write each equation in standard form. Identify
  A, B, and C.
  44. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  zero.
  Find the x-intercept and the y-intercept of the
  graph of each equation.
  47. A = 1, B = 6, and C = 7.
  SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  45. SOLUTION: The standard form of a linear equation is Ax + By =
  C, where A, B, and C are integers with a greatest
  common factor of 1,
  , and A and B are not both
  eSolutions
  The x-intercept is the value of x when y = 0.
  Replace y with 0.
  Page 11
  So, the y-intercept is 5.25.
  2-2 Linear Relations and Functions
  Find the x-intercept and the y-intercept of the
  graph of each equation.
  48. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  47. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  Replace y with 0.
  The x-intercept is the value of x when y = 0.
  Replace y with 0.
  So, the x-intercept is –10.5
  .
  The y-intercept is the value of y when x = 0.
  Replace x with 0.
  So, the x-intercept is –7.5.
  The y-intercept is the value of y when x = 0.
  Replace x with 0.
  So, the y-intercept is –1.25.
  49. So, the y-intercept is 5.25.
  SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  The x-intercept is the value of x when y = 0.
  The x-intercept is the value of x when y = 0.
  Replace y with 0.
  Page 12
  2-2 Linear
  Relations and Functions
  So, the y-intercept is –1.25.
  49. SOLUTION: The y-coordinate of the point at which a graph
  crosses the y-axis is called the y-intercept.
  Likewise, the x-coordinate of the point at which it
  crosses the x-axis is called the x-intercept.
  So, the y-intercept is
  .
  50. FUNDRAISING The Freshman Class Student
  Council wanted to raise money by giving car washes.
  The students spent \$10 on supplies and charged \$2
  per car wash.
  a. Write an equation to model the situation.
  b. Graph the equation.
  c. How much money did they earn after 20 car
  washes?
  The x-intercept is the value of x when y = 0.
  Replace y with 0.
  d. How many car washes are needed for them to
  earn \$100?
  SOLUTION: a. Let c be the number of cars and E be the
  earnings.
  So:
  E = 2c – 10
  b.
  So, the x-intercept is
  .
  The y-intercept is the value of y when x = 0.
  Replace x with 0.
  c. Replace c with 20.
  They earned \$30 by washing 20 cars.
  d. Replace E with 100.
  So, the y-intercept is
  .
  50. FUNDRAISING The Freshman Class Student
  Council wanted to raise money by giving car washes.
  The students spent \$10 on supplies and charged \$2
  per car wash.
  a. Write an equation to model the situation.
  They need to wash 55 cars to earn \$100.
  the13
  51. MULTIPLE REPRESENTATIONS Consider
  Page
  following linear functions.
  2-2 Linear
  Relations and Functions
  They need to wash 55 cars to earn \$100.
  ; the y -intercept is 5, the x-intercept
  is -15.
  51. MULTIPLE REPRESENTATIONS Consider the
  following linear functions.
  a. GRAPHICAL Graph the linear functions on
  separate graphs.
  b. TABULAR Use the graphs to complete the table
  b. Analyze the graphs of each function to determine
  whether they are one-to-one or onto.
  c. VERBAL Are all linear functions one-to-one
  SOLUTION: a. Use the intercepts to graph each equation.
  f(x) = -2x + 4; The y-intercept is 4, the x-intercept is
  2.
  c. No; horizontal lines are neither one-to-one nor onto
  because only one y-value is used and it is repeated fo
  every x-value. Every other linear function is one-toone and onto because every x-value has one unique y
  value that is not used by any other x-element and
  every possible y-value is used.
  52. CHALLENGE Write a function with an x-intercept
  of (a, 0) and a y-intercept of (0, b).
  SOLUTION: Sample answer: Use the x- and y-intercepts to
  determine the slope of the function. Since the y -
  g(x) = 6; the y -intercept is 6, there is no x-intercept.
  intercept is (0, b), the function will be in the form . Find m using the x-intercept. Let
  f(x) = 0 and x = a. Solve for m.
  The function is
  ; the y -intercept is 5, the x-intercept
  is -15.
  .
  53. OPEN ENDED Write an equation of a line with an
  x-intercept of 3.
  SOLUTION: Sample answer:An x-intercept of 3 means that when
  3 is substituted into the equation, y = 0. To writePage
  an 14
  equation, one factor should be (x - 3).
  f (x) = 2(x –3)
  2-2 Linear
  Relations
  The function
  is and Functions
  .
  53. OPEN ENDED Write an equation of a line with an
  x-intercept of 3.
  SOLUTION: Sample answer:An x-intercept of 3 means that when
  3 is substituted into the equation, y = 0. To write an
  equation, one factor should be (x - 3).
  f (x) = 2(x –3)
  54. REASONING Determine whether an equation of
  the form x = a, where a is a constant, is sometimes,
  always, or never a function. Explain your reasoning.
  SOLUTION: Sample answer: Never; the graph of x = a is a
  vertical line. Therefore it will always fail the vertical
  line test, for any value of a.
  55. CCSS ARGUMENTS Of the four equations
  shown, identify the one that does not belong. Explain
  SOLUTION: y = 2xy; since it cannot be written in the form f (x) =
  mx + b, y = 2xy is not a linear function.
  56. WRITING IN MATH Consider the graph of the
  relationship between hours worked and earnings.
  a. When would this graph represent a linear
  b. Provide another example of a linear relationship in
  a real-world situation.
  SOLUTION: a. Sample answer: When the earnings are
  determined by a constant hourly wage, the total
  earnings can be represented by y = mx where m is
  the hourly wage.
  b. Sample answer: The relationship between the cost
  and the number of gallons of gasoline purchased.
  Within a transaction, the cost of gasoline is constant
  so the total cost and the number of gallons purchased
  are a linear relationship.
  57. Tom bought n DVDs for a total cost of 15n – 2
  dollars. Which expression represents the cost of each
  DVD?
  A
  B
  C
  D
  SOLUTION: y = 2xy; since it cannot be written in the form f (x) =
  mx + b, y = 2xy is not a linear function.
  56. WRITING IN MATH Consider the graph of the
  relationship between hours worked and earnings.
  a. When would this graph represent a linear
  b. Provide another example of a linear relationship in
  a real-world situation.
  SOLUTION: a. Sample answer: When the earnings are
  determined by a constant hourly wage, the total
  earnings can be represented by y = mx where m is
  the hourly wage.
  b. Sample answer: The relationship between the cost
  and the number of gallons of gasoline purchased.
  Within a transaction, the cost of gasoline is constant
  so the total cost and the number of gallons purchased
  are a linear relationship.
  SOLUTION: The cost of n DVDs is 15n –2.
  The cost of 1 DVD is
  The correct choice is C.
  .
  58. SHORT RESPONSE What is the complete solution
  of the equation?
  SOLUTION: The solution set is {–3, 9}.
  Page 15
  59. NUMBER THEORY If a, b, c, and d are
  consecutive odd integers and a b c d, how much
  greater is c + d than a + b?
  The cost of n DVDs is 15n –2.
  The cost of 1 DVD is
  .
  2-2 Linear
  Relations and Functions
  The correct choice is C.
  58. SHORT RESPONSE What is the complete solution
  of the equation?
  The correct choice is J.
  60. ACT/SAT Which function is linear?
  A
  B
  SOLUTION: C
  D
  E
  The solution set is {–3, 9}.
  SOLUTION: In a linear function, the exponent of the independent
  variable is less than or equal to 1, and the variable is
  not in the denominator of a fraction. The correct choice is E.
  59. NUMBER THEORY If a, b, c, and d are
  consecutive odd integers and a b c d, how much
  greater is c + d than a + b?
  F 2
  H4
  G6
  J 8
  SOLUTION: Let a = 2n + 1.
  So:
  State the domain and range of each relation.
  Then determine whether each relation is a
  function . If it is a function, determine if it is oneto-one, onto, both, or neither.
  61. Therefore:
  SOLUTION: The left side of the mapping is the domain and the
  right side is the range.
  D = {–4, –1, 8}, R = {3, 6, 9};
  The relation is not a function because –4 is mapped
  to both 3 and 9.
  The correct choice is J.
  60. ACT/SAT Which function is linear?
  A
  B
  C
  D
  eSolutions
  E
  SOLUTION: 62. SOLUTION: The members of the domain are the x-values of the
  relation while the members of the range are the yvalues.
  D = {–2, 1, 2, 4}, R = {1, 3, 5};
  Page 16
  D = {–4, –1, 8}, R = {3, 6, 9};
  The relation is not a function because –4 is mapped
  2-2 Linear
  to both Relations
  3 and 9. and Functions
  The function is both one-to-one and onto because
  each element of the domain is paired with a unique
  element of the range and each element of the range
  corresponds to an element of the domain.
  64. SHOPPING Claudio is shopping for a new
  television. The average price of the televisions he
  likes is \$800, and the actual prices differ from the
  average by up to \$350. Write and solve an absolute
  value inequality to determine the price range of the
  televisions.
  62. SOLUTION: Let x be the actual price of the television.
  So:
  SOLUTION: The members of the domain are the x-values of the
  relation while the members of the range are the yvalues.
  D = {–2, 1, 2, 4}, R = {1, 3, 5};
  This implies:
  Each element of the domain is paired with exactly
  one element of the range. So, the relation is a
  function.
  The function is onto because each element of the
  range corresponds to an element of the domain.
  The price of the televisions ranges from \$450 to
  \$1150.
  Evaluate each expression if a = –6, b = 5, and c
  = 3.6.
  65. 63. SOLUTION: The members of the domain are the x-values of the
  relation while the members of the range are the yvalues.
  SOLUTION: D = {–4, –3, 7}, R = {–2, –1, 9};
  Replace a with –6, b with 5, and c with 3.6.
  Each element of the domain is paired with exactly
  one element of the range. So, the relation is a
  function.
  The function is both one-to-one and onto because
  each element of the domain is paired with a unique
  element of the range and each element of the range
  corresponds to an element of the domain.
  66. 64. SHOPPING Claudio is shopping for a new
  television. The average price of the televisions he
  likes is \$800, and the actual prices differ from the
  average by up to \$350. Write and solve an absolute
  value inequality to determine the price range of the
  televisions.
  SOLUTION: eSolutions
  Let x be the actual price of the television.
  SOLUTION: Replace a with –6, b with 5, and c with 3.6.
  Page 17
  The number of large pizzas with different onetopping = 3.
  2-2 Linear Relations and Functions
  Total = 9
  Evaluate each expression.
  66. SOLUTION: 69. SOLUTION: Replace a with –6, b with 5, and c with 3.6.
  67. SOLUTION: 70. SOLUTION: Replace a with –6, b with 5, and c with 3.6.
  71. 68. FOOD Brandi can order a small, medium, or large
  pizza with pepperoni, mushrooms, or sausage. How
  many different one-topping pizzas can she order?
  SOLUTION: SOLUTION: The number of small pizzas with different onetopping = 3.
  The number of medium pizzas with different onetopping = 3.
  The number of large pizzas with different onetopping = 3.
  72. SOLUTION: Total = 9
  Evaluate each expression.