Vocabulary
What is the term for a relationship between two quantities that have a constant ratio?
Proportional Relationship
What point must every proportional relationship pass through on a graph?
BONUS: What does the constant of proportionality represent in a graph?
The origin (0,0)
BONUS: The slope or the unit rate (change in y per 1 change in x).
What is the equation form used to represent a proportional relationship?
y = kx
If x = 2, 4, 6 and y = 4, 8, 12, is the relationship proportional?
Yes, y/x = 2
True or False: Every proportional relationship forms a straight line.
TRUE
What is the better deal:
$3.80/2 = $1.90
$2.70/1.5 = $1.80
The better deal by 10 cents is 1.5 liters of milk at $2.70
What anime was Ms. Hunter's halloween costume from?
BONUS: What is the characters name?
Demon Slayer
BONUS: Kyojuro Rengoku
What letter is usually used to represent the constant of proportionality?
k
What shape does a proportional relationship make on a graph?
a straight line
If y = 8x, what is the constant of proportionality?
k = 8
From Cara’s flower table: white (3, 6, 9) → yellow (5, 10, 15). Write the equation.
y = (5/3)w
If y/x = 2.5, what is the constant of proportionality?
2.5
Natalie walked 35 miles in 12 hours. What is her unit rate?
Approximately 2.9 miles per hour
What is Ms. Hunters favorite holiday?
Halloween!
What is a unit rate?
How much of something per 1 unit of something else.
If a graph passes through (0, 0) and (5, 20), what is the constant of proportionality?
k = 4
Write an equation showing g is proportional to t with k = 0.4.
g = 0.4t
What does the constant of proportionality tell you in Cara’s table?
REMINDER: white (3, 6, 9) → yellow (5, 10, 15).
There are 5 yellow flowers for every 3 white flowers.
If x = 3 and y = 9, what is the equation that relates y and x?
Sarah used 2.5 cups of cheese for 10 servings. How much per serving?
0.25 cups per serving
Will Ms. Hunter be chaperoning SOS (students on snowboards)?
YES!
What is a proportion?
Proportion says that two ratios (or fractions) are equal.
What does the ordered pair (3, 15) represent if x = hours and y = miles?
After 3 hours, 15 miles were traveled.
A faucet fills 2 gallons in 5 seconds. Write an equation for this relationship.
y = (2/5)x
From Hector’s flower table: white (4, 8, 12) → yellow (6, 10, 14). Is it proportional?
No, because y/x is not constant.
Explain why the relationship y = 5x + 2 is not proportional.
Because it doesn’t pass through the origin; the +2 breaks proportionality.
Arun used 1.6 cups for 8 servings. How much per serving? How does it compare to Sarah’s?
0.2 per serving; Sarah uses 0.05 more per serving.
How many countries do you think Ms. Hunter has traveled to? (closest answer wins)
BONUS: How many states do you think Ms. Hunter has NOT been to? (closest answer wins)
I have traveled to 11 countries, I am about to go to 2 more this upcoming summer!
BONUS: I have NOT been to about 14-15 of the states.
What is an equivalent proportion?
When quantities have the same relative size. In other words they have the same ratio.
A line passes through (10, 400) and (20, 800). Is the relationship proportional? Explain.
Yes, because the ratio y/x is constant (400/10 = 800/20 = 40).
The equation for a relationship is t = 2.5g. What is another equivalent form of this equation?
2.5 = t/g
OR
t/g = 2.5
How can you tell if a table is not proportional?
The ratios of y/x are not equal or the graph doesn’t pass through (0, 0).
A graph shows a line through (0, 0) and (8, 20). Is it proportional? Find k and the equation.
Yes, k = 20/8 = 2.5; equation y = 2.5x.
Ariel bought 2 cookies for $1.50. What’s the unit rate, and what does the point (1, 0.75) represent?
$0.75 per cookie; (1, 0.75) means 1 cookie costs $0.75.
Who is Ms. Hunter dating?
Who is Mr. Curry?