Linear Functions

Linear Functions

Review for Test

Multiple Choice

Create the explicit formula for the sequence:

2, 8, 14, ...

(Hint: Write your formula and then simplify it.)

• f(n)=2+6n

• f(n)=-6+6n

• f(n)=6n-4

• f(n)=4-6n

Multiple Choice

Write the EXPLICIT rule for the arithmetic sequence

9, 13, 17, 21, ...

• f(n) = -4n + 5

• f(n) = -9n + 14

• f(n) = 9n - 5

• f(n) = 4n + 5

Multiple Choice

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

• f(n) = 10n + 17

• f(n) = 7n - 17

• f(n) = -7n + 17

• f(n) = 7n + 3

Multiple Choice

Write the RECURSIVE rule for the arithmetic sequence

-49, -35, -21, -7, ...

• f(1)=-49;

  f(n) = f(n-1) + 10

• f(1)=-7;

  f(n)=f(n-1) + 14

• f(1)=-49;

  f(n) = f(n-1) + 14

• f(1)= -49;

  f(n) = f(n-1) -14

Multiple Choice

Is this graph a linear or nonlinear function?

• nonlinear
• linear

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Which graph(s) show nonlinear functions?

• Graph I, only
• Graph II, only
• Graph I and Graph II, only.
• Graph I, Graph II, and Graph III

Multiple Choice

Is this function linear or nonlinear?

• Linear function
• Nonlinear function

Multiple Choice

Why is this function nonlinear?

• This function is nonlinear because it has a constant rate of change.
• This function is nonlinear because it does not have a constant rate of change.
• The function is nonlinear because the y-intecept is (0,1)
• This function is nonlinear because there is a coefficient of 4.

Multiple Choice

Is this function linear or nonlinear?

• linear
• nonlinear

Multiple Choice

Is this function linear or nonlinear?

• linear
• nonlinear

Multiple Choice

Solve for y: 
4x + 3y = 9

• y = -3/4x + 3
• y = -4x + 9
• y = -4/3x + 3
• 3y = -4x + 9

Multiple Choice

Solve for y:
2x + 2y = 6

• y = - x + 3
• y = x + 3
• y = 2x +6
• y = - 2x + 6

Multiple Choice

Solve for y: 
3x + y = 12

• y = -3x +12
• x = y + 4
• x = y + 12
• y = 3x -12

Multiple Choice

Solve for y:
5x + y = -10

• y = 5x + 10
• y = -5x - 10
• y = 2
• y = -5

Multiple Choice

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

• -1, 7, 15
• -5, 2, 9
• 3, 12, 21
• -65, -73, -81

Multiple Choice

Find the common difference: -34, -29, -24, -19, ...

• d = -5
• d = 5
• d = -6
• d = 6

Multiple Choice

Is the sequence arithmetic: 17, 9, 1, -7, ...

• Yes
• No

Multiple Choice

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

• Yes
• No

Multiple Choice

Choose the graph that matches the story:

Ava was jogging to the store. She realized that she had dropped her wallet, so she walked partway back home until she found her wallet. Then she turned around and jogged to the store.

• Graph A

• Graph B

• Graph C

• Graph D

Multiple Choice

Paco's daughter will be participating in an upcoming dance recital. She will require a different costume for each dance she plans to performs.
c = the number of costumes Paco's daughter will require
d = the number of dances Paco's daughter plans to perform
Which of the variables is independent?

• c
• d

Multiple Choice

The function c(m) = 1.45m + 3.50 represents the cost of a taxi for m miles.
What does c(m) represent?

• Total Cost of a taxi
• Total Miles in taxi

Multiple Choice

Carey and Justin are raising money to purchase books for their school's library. The more money they raise, the more books they will be able to purchase for the library.
m = the amount of money Carey and Justin raise
b = the number of books Carey and Justin will be able to purchase
Which of the variables is dependent?

• m
• b

Multiple Choice

What does H(5) =18 mean in the context of the problem?

• The height of the plant after 5 weeks is 18 inches

• The height of the plant after 18 weeks is 5 inches

• The height of the plant is 5 inches after 18 weeks

• The height of the plant is dependent on the week it was planted

Multiple Choice

What does f(1990)=214 mean in the context of the problem?

• In 1990 there were 214 million people with health insurance

• In 214, there were 1990 people with health insurance

• When there are 1990 people, the year is 214

• None of these

Multiple Choice

The function d(x) where x=gallons of gas and d(x)= # of miles traveled.
Interpret d(8)=300 in context.

• A car with 8 gallons of gas can travel 300 miles.
• A car traveling 8 miles has 300 gallons of gas.
• A car is traveling 300 miles.
• The car traveling 8 mph can go 300 miles.

Multiple Choice

Derek works at Subway making $9.25 an hour.  The function d(x)=9.25x tells us how much money Derek makes after x hours of working.  What is the meaning of d(4)=37?

• After 4 hours of work, Derek makes $37.
• Derek needs $4 more to have $37 total.
• After working for 4 days, Derek makes $37 total.
• After 4 hours of work, Derek now makes $37 an hour instead of $9.25.

Multiple Choice

The function c(m) = 1.45m + 3.50 represents the cost of a taxi for m miles.
What does c(7) represent?

• A cost of $7 to ride the taxi
• The cost to ride 7 miles
• The minimum distance to ride a taxi
• The minimum cost of a taxi

Multiple Choice

The function h(t) represents the height in inches of a plant after t weeks. What does the notation h(4) = 5 mean?

• After 5 week the plant is 4 inches tall
• The plant grows at a rate of 5/4 inch per week
• After 4 weeks the plant is 5 inches tall
• The plant grows at a rate of 1 inch per week

Multiple Choice

A man is climbing down from 100 feet high descending 30 feet per minute.

• y = 100 - 30x
• y = 100 + 30x
• y = 100x + 30
• y = 100x - 30

Multiple Choice

Bob has $150 in his savings account and saves $40 per month.

• y = 150 + 40
• y = 40x + 150
• y = 150x + 40

Multiple Choice

Bob's Plumbing charges $15 per hour plus a service fee of $40 for coming out to your house. Which equation models this situation?

• y = 15x + 40

• y = 40x + 15

• y = 15x

• y = 15x - 40

Multiple Choice

Lisa went to the mall to do her back-to-school shopping.  When she returned, she noticed that the number of shirts (s) she purchased was 3 more than twice the number of pants (p) she bought.  What is an equation that can be used to represent the number of shirts Lisa purchased? 

• p=3 + 2s
• s + 2p =3
• s = 3 + 2p
• 2p = s + 3

Multiple Choice

The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of airtime usage.  If Juanita uses x minutes of airtime, what is an equation that can be used to determine her monthly cell phone bill (C)?

• C = 15 + 0.20x
• C =15 (0.20x)
• C = 15 + x + 0.20
• C = 0.20 + 15x

Multiple Choice

At Joe's Clown Car Rental Agency, renting a car costs $35 plus $0.75 for every mile it is driven.  What is an equation that can be used to find the number of miles, m, a vehicle was driven, if the total rental charge was $222.50?

• 222.5 = m(35 + 0.75)
• 222.5 = 35 + 0.75m
• 222.5 = 0.75 + 35m
• 222.5 = 0.75(m + 35)

Multiple Choice

Margaret is a waitress at The Seafood Bonanza.  She earns $3 an hour plus 90% of her tips.  Write an equation for her salary, S, if she works h hours and earns d dollars in tips.

• 3h + 0.90d = S
• S = 90d + 3h
• S = 3d + 90h
• S = 3h + 9.0d

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation for C, the total cost, to rent the boat for h hours.

• h = 2C + 15
• C = 15h + 2
• h = 15C + 2
• C = 2h + 15

Multiple Choice

What is the constant rate of change between the quantities in the table?

• $1 per hour

• $40 per hour

• $5 per hour

• $10 per hour

Multiple Choice

• 40 CALORIES PER MIN.
• 15 CALORIES PER MIN.
• 4 CALORIES PER MIN.
• 60 CALORIES PER MIN.

Multiple Choice

Which of the following are ways to find the rate of change?

• change in y over change in x
• rise over run
• subtract y coordinates over subtract x coordinates
• all of the above

Multiple Choice

Find the unit rate:  $3.60 for 3 pounds of apples. How much does it cost for 1 pound of apples?

• $1.00 per pound
• $3.60 per pound
• $1.20 per pound
• $1.10 per pound

Multiple Choice

At what rate did the rain fall?

• 2 cm per hour
• ¹/₄ cm per hour
• ¹/₂ cm per hour
• 4 cm per hour

Multiple Choice

What is the slope in this picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

What is the slope in the equation:  y=4x+3

• 3
• 4x
• 4
• x

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• nothing

Multiple Choice

Which of these represents slope-intercept form?

• y - y₁ = m(x-x₁)
• Ax + By = C
• y = mx + b

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

  Find the distance between (12, -5) and (2, -5).Round to the nearest tenth. 

• 14.1
• 10
• 8
• 14

Multiple Choice

Find the distance between (-3, -11) and (8, -42).

• 32.1
• 32.3
• 32.7
• 32.9

Multiple Choice

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

Multiple Choice

Given two points (x₁, y₁), (x₂, y₂) the distance between them is:

Multiple Choice

Find the distance between J and K.

• 8.2
• 7.7
• 9
• 10.2

Multiple Choice

What is the distance between the two points?

• 6.3
• 6.5
• 6.7
• 16

Multiple Choice

Becky leaves school to go home. She walks 6 blocks North and then 8 blocks west. How far is Becky from the school? 

• 14 blocks
• 12 blocks
• 10 blocks
• 8.5 blocks

Multiple Choice

Find the midpoint:

• $\left(-\frac{3}{2},-\frac{5}{2}\right)$

• $\left(-1,-3\right)$

• $\left(-\frac{1}{2},-\frac{5}{2}\right)$

• $\left(-3,-1\right)$

Multiple Choice

Find the midpoint:

• 
  

  $\left(3,-1\right)$
  

• $\left(-1,3\right)$

• $\left(3,4\right)$

• $\left(4,3\right)$

Multiple Choice

What is the midpoint of the segment with endpoints (1, 9) and (-3, 5)?

• (-1, 7)

• (2, 7)

• (7, -1)

• (2, 2)

Multiple Choice

What is the midpoint between (-4,4) and (-2,2)?

• (3,2)
• (-3,3)
• (4,5)
• (6,7)

Multiple Choice

What is the midpoint between (3, -1) and (7, -5)

• (5, -2)
• (10, -6)
• (5, -3)
• (2, -2)

Multiple Choice

Find the y-coordinate of the midpoint of the line

• 1
• 2
• -2
• 3

Multiple Choice

Find slope:

• m= 4
• m=1/4
• m=-4
• m=-1/4

Multiple Choice

Find the value of y when x = 2.

• 2
• 6
• 7
• 8

Multiple Choice

What is the y-intercept?

• 7
• 0
• 1
• 2

Multiple Choice

What is the y-intercept for the given graph?

• (0,-5)

• (0,5)

• (0,1)

• (0,-1)

Multiple Choice

What is the y-intercept in the equation?

y = 5x - 4

• (0,5)

• (0,-4)

• (-4,0)

• (5,0)

Multiple Choice

What is the equation for this graph? 

• y=-1x+0
• y=1/2x+0
• y=2x+0
• y=-2x+0

Multiple Choice

Consider the equation:
y=-x+4
Identify the slope and y-intercept.

• m=4, b=-x
• m=-x, b=4
• m=1, b=4
• m=-1, b=4

Multiple Choice

Which is the graph of y= -x + 2?

• A
• B
• C
• D

Multiple Choice

Write the equation for the line

•  y=⅗x+1
•   y=⅗x-1
•  y=(5/3)x+1
• y=(3/5)x+1

Multiple Choice

What is the slope of the equation?
y = -3x + 4

• -3
• 3
• 4
• -4

Multiple Choice

In the equation, y = mx + b, the letter b is the ___________.

• y-intercept
• x-intercept
• slope
• rate of change

Multiple Choice

Writing Equations:
Given the following table, write the linear equation.

• y = 9x + 3
• y = 3x + 12
• y = 3x + 9
• y = 1x + 12

Multiple Choice

Which equation is being represented by this line?

• y = -1x + 2
• y = 1/2x + 2
• y = 3x -4
• y = -3x +2

Multiple Choice

Does this mapping diagram represent a function?

• No, because there are repeating input values
• Yes, because there are no repeating input values

Multiple Choice

Which equation matches the table?

• y=2x
• y=x-3
• y=x+2
• y=1/2x

Multiple Choice

What equation does the table represent?

• y=x+1
• y=x-1
• y=2x+1
• y=2x-1

Multiple Choice

When you have a vertical line, you have a slope that's _______

• Zero 
• Undefined 
• One
• Ten

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Which graph is linear?

• Graph A
• Graph B
• Graph C
• Graph D

Multiple Choice

Find the slope between the two given points: (-2,1) and (5,7)

• 7/6
• 2
• 6/7
• -2

Multiple Choice

Transform from standard form to slope intercept form:    2x-3y=10

• y=-2x+10
• y= 2/3x-10/3
• y=-2/3x+ 10/3
• y=2/3x+10