Example 1:
Problem: If you earn $15 for every hour you work, how much will you earn after working
for 7 hours?
Solution: Here, the constant of proportionality ( k ) is $15 per hour. The relationship
between the money earned ( y ) and the hours worked ( x ) is y = 15 x . Plugging in the value of
x : y = 15 \times 7 = 105 So, you will earn $105 after working for 7 hours.
Example 2:
Problem: A car travels at a constant speed of 60 miles per hour. How far will the car
travel in 3 hours?
Solution: Here, the constant of proportionality (k) is 60 miles per hour. The relationship
between the distance traveled (y) and the time (x) is y=60x. Plugging in the value of x: y = 60
times 3 = 180 So, the car will travel 180 miles in 3 hours.
Example 3:
Problem: A recipe calls for 2 cups of flour to make 12 cookies. How many cups of flour
are needed to make 36 cookies?
Solution: Here, the constant of proportionality ( k ) is the number of cups of flour per
cookie. The relationship between the cups of flour ( y ) and the number of cookies ( x ) is
y = 2/12 x = 1/6 x . Plugging in the value of x : y = 1/6 times 36 = 6 So, you will need 6
cups of flour to make 36 cookies.
Problem: If you earn $15 for every hour you work, how much will you earn after working
for 7 hours?
Solution: Here, the constant of proportionality ( k ) is $15 per hour. The relationship
between the money earned ( y ) and the hours worked ( x ) is y = 15 x . Plugging in the value of
x : y = 15 \times 7 = 105 So, you will earn $105 after working for 7 hours.
Example 2:
Problem: A car travels at a constant speed of 60 miles per hour. How far will the car
travel in 3 hours?
Solution: Here, the constant of proportionality (k) is 60 miles per hour. The relationship
between the distance traveled (y) and the time (x) is y=60x. Plugging in the value of x: y = 60
times 3 = 180 So, the car will travel 180 miles in 3 hours.
Example 3:
Problem: A recipe calls for 2 cups of flour to make 12 cookies. How many cups of flour
are needed to make 36 cookies?
Solution: Here, the constant of proportionality ( k ) is the number of cups of flour per
cookie. The relationship between the cups of flour ( y ) and the number of cookies ( x ) is
y = 2/12 x = 1/6 x . Plugging in the value of x : y = 1/6 times 36 = 6 So, you will need 6
cups of flour to make 36 cookies.
