Under partial variation :x is partly constant and partly varies with y ,when y=3, x=7 and when y=6, x=9.find the relationship between x and y
x = ay+b
using the two data points, you have
3a+b = 7
6a+b = 9
clearly, a = 2/3
so now find b.
Well, it seems like x is being quite indecisive here - partly constant and partly varying with y. It's like having a split personality! But don't worry, I'll try to figure out the relationship between x and y.
Let's start with the given values. When y = 3, x = 7. And when y = 6, x = 9.
Now, let's analyze this situation. When y goes up by 3 from 3 to 6, x increases by 2 from 7 to 9. That's interesting.
So, it looks like x increases by 2 units for every 3 units that y goes up.
To put it in mathematical terms, we can say that the relationship between x and y is:
x = (2/3) * y
There you have it, x and y are in a slightly quirky relationship where x is partly constant and partly varies with y. Isn't math fascinating?
To find the relationship between x and y under partial variation, we can use the formula:
x = k * y
where k is the constant of variation.
Given that when y=3, x=7 and when y=6, x=9, we can substitute these values into the formula to solve for k.
When y = 3 and x = 7:
7 = k * 3
When y = 6 and x = 9:
9 = k * 6
We can solve this system of equations to find the value of k.
Multiplying the first equation by 2, we have:
14 = 2k * 3
Simplifying, we get:
14 = 6k
Dividing both sides by 6:
k = 14/6 = 7/3
Therefore, the relationship between x and y under partial variation is:
x = (7/3) * y
To find the relationship between x and y under partial variation, we need to determine the constant part and the varying part.
Given that when y = 3, x = 7, and when y = 6, x = 9, we can see that the constant part is when x remains the same regardless of changes in y.
Let's find the constant part:
- When y = 3, x = 7
- When y = 6, x = 9
From these two sets of values, we can see that when y changes from 3 to 6, x changes from 7 to 9. Therefore, the constant part is 7.
Now, let's find the varying part:
- When y = 3, x = 7
- When y = 6, x = 9
From these two sets of values, we can see that when y changes from 3 to 6, x changes from 7 to 9. Therefore, the varying part is 2.
To find the relationship between x and y, we can express it as:
x = constant part + (varying part * y)
Substituting the values we found:
x = 7 + (2 * y)
Hence, the relationship between x and y under partial variation is x = 7 + (2 * y).