Proportional Relationships
Proportional Graphs
Constant of Proportionality
Unit Rate and Equations
Slope
100
Is the relationship between the number of miles driven and the amount of gas used a proportional relationship? Why or why not?
Yes, because the ratio of miles to gallons is constant.
100
What does the point (0,0) represent in a graph of a proportional relationship?
It represents that when the input is 0, the output is also 0, indicating a proportional relationship. When X = 0, Y= 0.
100
What is the unit rate if 10 oranges cost $5?
$0.50 per orange
100
The equation y = 5x can be used to determine the total cost, (y), in dollars, of (x) pounds of bananas. What does the number 5 represent in the equation?
A. The number of bananas in 1 pound
B. The number of bananas in (x) pounds
C. The cost of 1 pound of bananas
D. The cost of (y) pounds of bananas
C. The cost of 1 pound of bananas.
100
Are all the lines proportional and which color is traveling faster?
Yes, they are proportional because they all go through the origin (0,0).
Green is traveling the fastest because the slope of green is steeper than red and blue.
200
If a recipe calls for 2 cups of flour for every 3 cups of sugar, is this a proportional relationship? Why or why not?
Yes, because the ratio of flour to sugar is constant.
200
If a proportional graph shows the cost of apples per pound, and the point (5,10) is on the graph, what is the cost per pound?
$2 per pound
200
If a car travels 200 miles in 4 hours, what is the constant of proportionality for the distance traveled per hour?
The constant of proportionality is 50 miles per hour.
200
Write an equation to represent the situation.
y = 2.5x
Bonus Points: What does the number 2.5 represent?
200
If the line passes through the points (1,2) and (4,8), what is the slope of the line?
2
300
Complete the following to make a TRUE statement.
The quantities represented in the table _____ (are, are not) in a proportional relationship. The equation _____ can be used to represent the relationship.
The quantities represented in the table are in a proportional relationship. The equation y = 5x can be used to represent the relationship.
300
If the graph shows the relationship between the number of books read and the number of weeks, is the point (4.5, 8) on the graph?
No, the point (4.5, 8) is not on the graph because it does not lie on the line representing the relationship. The CoP is 2 in the graph and 4.5(2) is 9, not 8.
300
What is the Constant of Proportionality?
The constant of proportionality is 3.
300
The equation y = 3.75x can be used to determine the total cost, (y), in dollars, of (x) gallons of milk. What does the number 3.75 represent in the equation?
The cost of 1 gallon of milk.
300
If slope is y/x, what is the slope on the graph?
1/2 or 0.5
400
Determine if the relationship between the number of hours worked and the total pay is proportional. Explain your reasoning.
Yes, the pay rate per hour is constant. The line is straight and goes through the origin (0,0)
400
If a graph shows the relationship between the number of hours studied (x) and the test scores (y), and the line passes through (2,80), what does this point represent?
It represents that studying for 2 hours results in a test score of 80.
400
If 8 gallons of paint covers 32 square feet, what is the constant of proportionality?
The constant of proportionality is 4 square feet per gallon.
400
Which statement about the graph is TRUE if the equation is y = 3x
A. The point (4,12) shows that the cost is $12 for 4 units.
B. The point (4,12) shows that the cost is $4 for 12 units.
C. The slope of the line is 1/3
D. The slope of the line is -1/3
A. The point (4,12) shows that the cost is $12 for 4 units.
400
What is the slope of the line that passes through the points (2,8) and (6,24)?
4
500
Is the relationship between the number of books read and the number of days a proportional relationship? Why or why not?
No, because the number of books read per day is not constant.
500
A. If the gear rotates 30 times, then it has been rotating for 1.5 minutes.
500
Odd Man Out: Find the Constant of Proportionality for each one. Which one doesn't match with the others?
y = 1/3x
All the others have a CoP of 3.
500
Kel walked at a constant speed. He walked 1 mile in 16 minutes. Which of these equations represents the distance D (in miles) that Kel walks in T minutes?
d = 16t
d = t + 16
d = 1/16t
d = t + 16
d = 1/16t
500
Determine the slope of the line that passes through the points (3,9) and (8,19).
Think change in y / change in x
2