check if x and y vary directly in the following
x. 2. 14. 20. 22. 26
y. 7 21. 28. 35. 49
Answers
Answer
No, x and y don't vary directly i.e. x and y are not directly proportional to each other.
Explanation
Overview:
Direct proportions refers to the relation between two variables, where if variable 1 increase with a factor of k then variable 2 will also increase with the factor of k and vice versa.
Or in other words,
If the ratio of the different values of variable 1 and variable 2 is a constant value, the two variables are in direct proportion.
Solution:
The given values of x
- x₁ = 2
- x₂ = 14
- x₃ = 20
- x₄ = 22
- x₅ = 26
The given values of y
- y₁ = 7
- y₂ = 21
- y₃ = 28
- y₄ = 35
- y₅ = 49
Now, let's see if the ratio of the corresponding values of x and y is a constant value.
- x₁ /y₁ = 2/7
- x₂ /y₂ = 14/21 = 2/3
- x₃/y₃ = 20/28 = 5/7
- x₄/y₄ = 22/35
- x₅ /y₅ = 26/49
If x and y were in direct proportion we should have got the results like this:
x₁ /y₁ = x₂ /y₂ = x₃/y₃ = x₄/y₄ = x₅ /y₅
But According to what we got:
x₁ /y₁ ≠ x₂ /y₂ ≠ x₃/y₃ ≠ x₄/y₄ ≠ x₅ /y₅
So, x and y do not vary directly with each other.