Constant of proportionality
Find the Constant of Proportionality
A bicycle travels 36 miles in 3 hours at a constant rate. What is the constant of proportionality k. (miles per hour)
k=12 miles per hour
True or False: In a proportional relationship the ratio y/x is always the same for every pair of values.
True
A student reads 24 pages in 3 hours.
Question: How many pages does the student read per hour?
24÷3=8
8 pages per hour
The relationship between x and y is proportional.
Complete the table:
X 2 5 8
Y 10 ? ?
X 2 5 8
Y 10 25 40
Sam buys apples two bags of apples the first has 6 apples and costs 30 dollars, and the second has 8 apples and costs 45 dollars.
Is the ratio a proportional relationship?
No
30÷6 = 5
45÷8 = 5.625
A pack of 8 pencils costs $4.
Question: What is the cost of 1 pencil?
4÷8=0.5
$0.50 per pencil
Write an Equation
A recipe uses 4 cups of flour(y) for every 10(x) cookies.
y=0.4x
A babysitter earns $45 for 3 hours.
What will they make if they work 6 hours?
$90
3 x 2 = 6
45 x 2 = 90
A train travels 180 miles in 4 hours.
Question: What is the train's speed in miles per hour?
180÷4=45
45 miles per hour
Do proportional relationships always form a straight line on a graph?
Yes all proportional relationships create a straight line on a graph.
A runner's distance is proportional to the time spent running. After 6 minutes, the runner has traveled 0.9 miles.
What is the constant of proportionality?
k = 0.9÷6 = 0.15 miles per minute
A gym charges a proportional monthly fee. If a member pays $24 for 3 months, which equation represents the relationship between the cost y and the number of months x?
A. y=8x
B. y=21x
C. y=27x
24÷3=8
y=8x
A recipe uses 6 cups of flour to make 8 servings.
Question: How many cups of flour are needed for 1 serving?
6÷8=0.75
0.75 cups per serving
Do all proportional relationships pass through (0,0) on a coordinate plane?
Yes all proportional relationships pass through (0,0), the origin point.
A store charges proportionally for apples. A customer pays $7.50 for 5 pounds of apples.
Find the constant of proportionality (cost per pound).
How much would 12 pounds of apples cost?
k = 7.50÷5 = 1.50 dollars per pound.
12 pounds of apples costs 18 dollars.
If (4,12) is a point in a proportional relationship between x and y, which equation represents the relationship?
A. y=8x
B. y=4x
C. y=3x
12÷4=3
y=3x
A runner travels 2.5 miles in 20 minutes.
Question: What is the runner's unit rate in miles per minute?
2.5÷20=0.125
0.125 miles per minute
True or False:
A graph contains the point (5,15) and passes through the origin is has a proportional relationship?
True a graph that passes through (0,0) and forms a straight line has a proportional relationship.