Question:
The quantities x and y are proportional.
x 15 25
y 5 8⅓
Find the constant of proportionality.
Answer:
r = ⅓
Step-by-step explanation:
To find the constant of proportionality, we make use of the following formula
y = rx
Where y is the given data in the y row
r is the constant of proportionality
x is the given data in the x row.
Using the first values of x and y.
When x = 15, y = 5.
So,
y = rx becomes
5 = r * 15
5 = 15r
Divide through by 15
5/15 = 15r/15
⅓ = r
r = ⅓
Taking the second values of x and y
when x = 25, y = 8⅓
So,
y = rx becomes
8⅓ = r * 25
8⅓ = 25r
Convert mixed fraction to improper fraction
25/3 = 25r
Divide through by 25
25/3 ÷ 25 = 25r/25
25/3 * 1/25 = r
25/75 = r
⅓ = r
r = ⅓
Notice that r = ⅓ is the same for both values of x and y.
Hence, the constant of proportionality is ⅓