Constant of Proportionality
Writing Equations form Situations
Rate of Change
Graphs, Tables, Equations
Equations, Inequalities, and
Number lines
Number lines
100
Mason and his family drove 6 hours every day during their Fall Break road trip. How many hours will Mason and his family have driven after 3 days? Write your answer as an order pair.
What is 18 hours? (3, 18)
100
A boat rental costs more the further you travel. Boat rentals usually charge a fee on top of the per-mile charge to cover rental of the vehicle. In this case, the boat rental charges $3 as a set fee and $0.80 per mile traveled. What is the equation to represent cost in dollars(y) to rent a boat and the distance traveled in miles (x)?
What is y=0.80x+3 ?
100
A botanist is tracking the growth of a sunflower seedling over several weeks. The table below shows the height of the seedling, H, in centimeters, measured at the end of week t. What is the average rate of change?
What is 4.5 cm per week?
100
A student in a foreign language program learns 15 new words each week. Which graph best represents the relationship between x, the number of weeks the student has been in the program and y, the total number of new words the student has learned?
A 
B
C 
D
A-
100
Solve the following inequality and graph.
4x-7>=5
What is x>=3 ?
200
A tank is filling with water. After 2 minutes, it contained 14 gallons. After 5 minutes, it contained 35 gallons.
What is the constant of proportionality that relates the gallons, y, to the time in minutes, x, represented by the data?
What is 7?
200
The Student Council is organizing a charity fun run. Participants are asked to get sponsors who will pledge a flat donation plus an additional amount for every mile run.
Mark's grandfather pledged a flat donation of $25.00 to the charity. In addition, he promised to donate $1.50 for every mile Mark runs during the event. Write am equation that models the total donation, D, Mark's grandfather will make as a function of the number of miles Mark runs, m.
What is y=1.50x+25 ?
200
A water management team is monitoring the volume of water in a local reservoir during a dry season. The table below shows the reservoir's volume, V, in cubic meters (m3), measured at the beginning of day d. What was the average rate of change of the reservoir's water volume, in cubic meters per day?
What is -6 m3 per day?
200
A person burning 300 calories in 25 minutes on the elliptical. Which equations, tables or graphs show the relationship between the number of minutes, x, and the total calories, y? Select TWO correct answers.
A. y=12+x
B. y=12x
C. 
D. 
What is B and D?
y=12x 
200
Solve for x.
4x+2=-50
What is -13?
300
The cost of 3 pounds of grapes is $6.57. The cost of 5 pounds of grapes is $10.95. What is the constant of proportionality that relates the cost in dollars, y, to the number of pounds of grapes, x?
What is $2.19?
300
A mobile phone provider offers a monthly plan to its customers. The plan has a fixed monthly fee of $35.00 which includes unlimited talk and text. However, the plan charges an additional fee of $0.05 for every megabyte (MB) of data a customer uses over their monthly allowance. Write an equation that models the total monthly cost, C, a customer will pay as a function of the number of megabytes of excess data used, d.
What is y=0.05x+35 ?
300
A research submarine is descending into the ocean to study a deep-sea trench. At 2:00 PM, the submarine is at a depth of 100 meters below sea level. At 2:40 PM, the submarine has reached a depth of 600 meters below sea level. What was the submarine's average rate of change in depth in meters per minute during this 40-minute period?
What is 12.5 meters per minute?
300
Which equation represents the relationship between the x-values and the y-values in the table?
What is y=6x+4 ?
300
The model represents an inequality
What is the solution set for the inequality?
x<=-4
400
A baker is making large batches of chocolate chip cookies. The table below shows the relationship between the number of batches made, B, and the total number of cups of flour needed, F. If the relationship is proportional, find the constant of proportionality.
What is 2.5 cups of flour for every batch?
400
During a cold front, a town's temperature began to fall rapidly. At 9:00 AM, the temperature was recorded at 50∘F. The weather service predicts the temperature will continue to drop at a steady rate of 3∘F every hour. Write a linear equation that models the town's temperature, T, in degrees Fahrenheit, as a function of the number of hours, h, after 9:00 AM.
What is T=-3h+50 ?
400
The graph below represents the height, H (in feet), of a section of a new roller coaster over a horizontal distance, D (in inches), from the start of the section. The graph shows a straight line segment between two key points. What is the rate of change of the roller coaster's height, in feet per inch, as it travels from Point A to Point B?
What is -1.75?
400
Which equation matches the graph?
What is y=1/2x+1 ?
400
GRAPH the inequality
9x+9>36
x>3
500
The graph below shows the relationship between the number of bottles filled, N, and the time in seconds, t, for a water bottling machine. The relationship is known to be proportional. What is the constant of proportionality?
What is 4 bottles per second?
500
A local plumber, Bob, charges customers for his service call using a simple pricing model. He charges a one-time fixed fee of $60 just for showing up at the house, regardless of the time spent. In addition to this fixed fee, he charges $75 for every hour he spends working on the plumbing issue. Write an equation AND then calculate the total cost for a job that takes 3.5 hours.
What is y=75x+60 and $322.50?
500
What is the rate of change in the equation
y=-63.4x+187?
What is -63.4?
500
Brayden drives from San Francisco to Kansas City at a constant rate of 62 miles per hour. Which table represents y, the number of miles Brayden drives to x, the number of hours?
A.
B. 
C. 
What is B? 
500
What is the value of x?
-5(x+3)=15
What is -6?