Proportional Hodgpodge
Hunter jogs four miles in thirty minutes. Ryan jogs seven miles in forty-eight minutes. What is each person's rate of speed? Who jogs the fastest?
Hunter: 30min / 4miles = 7.5 minutes per mile
Ryan: 48 min / 7 miles ≈ 6.85 minutes per mile
Ryan is faster.
Is the table proportional? (table 1)
If yes, find the constant of proportionality.
No
Chris biked at a constant speed. He biked 1 mile in 5 minutes.
Which of these equations represents the distance 𝑑 (in miles) that Chris bikesin 𝑡 minutes?
A. 𝑑 = 𝑡 + 5
B. 𝑑 = 𝑡 − 5
C. 𝑑 = 5𝑡
D. 𝑑 = 1/5 t
c. d = 5t
A graph has a point at (7, 17.5).
Will the point (1, 2.50) be on this graph?
yes! 2.50 is the constant of proportionality!
A twelve-pack of Orange Crush is priced at $3.00. A six-pack is priced at $1.75. Which is the better value?
$3 / 12 cans = $0.25 per can
$1.75 / 6 cans ≈ $0.29 per can
12 cans is a better value
Is the table proportional? (table 2)
If yes, find the constant of proportionality.
K = 3
Does the equation show a proportional relationship? If yes, what is K?
y = 2x + 12
not proportional
Graph 1 shows the distance two cars are traveling over time. Which car is driving faster? Why?
Car B is traveling faster. Since it is steeper, it has a larger distance per hour.
Mario travels 180 miles in 2.5 hours. If Mario travels at the same rate, how far can Mario travel in 5 hours?
360 miles in 5 hours.
(K = 72 miles per hour)
True or False (with explanation). A table with a 0 in the x-column and 0 in the corresponding y-column can NOT be proportional.
False, the point is the origin and proportional relationships pass through the origin
Does the equation show a proportional relationship? If yes, what is K?
b = 0.75 m
yes
k = 0.75
What MUST be true of a graph for a proportional relationship (2 main expectations)
-passes through the origin
-is a straight line
Is there are proportional relationship between feet and inches? Prove it
Yes. Every foot is 12 inches. 12inches / 1 foot.
y = 12x
Complete the table (table 3) to show the proportional relationship between weight and bananas.
0.96 and 3.84
write an equation for and decide if it is proportional or not and identify what each variable means;
Jessica pays a $3 flat service fee plus $9 for each movie ticket she buys online.
y = 3 + 9x
y = money spent
x = number of movie tickets
Which of the graphs are proportional? Explain how you know. (graph 2)
None.
A- curved
B- not through origin
C- not through origin
During the fall, a pumpkin patch advertises four pumpkins for $16.00. Write two equations to represent this proportional relationship.
c = 4 p
p = 0.25 c
To find the constant of proportionality we should do column 1 ➗ column 2
We should do Column 2 ➗ column 1.
You CAN but you would be doing everything in the reciprocal!
write an equation for and decide if it is proportional or not and identify what each variable means;
John earns $12.50 per hour dog sitting his neighbors dog.
y = 12.50 x
y = money made
x =number of hours
proportional.
Write an equation for this line and explain what the points mean in this context. (graph 3)
L = 2/3 T
each lap takes 2/3 of a minute