X is partly constant and partly varies with y when y=3,x=11and when and when y=4,x=14

Question

A. Find the relationship between x and y
Find x when y=10

Answer 1

To find the relationship between x and y, we can first calculate the change in x for a change in y from 3 to 4.

When y=3, x=11
When y=4, x=14

The change in x for a change in y from 3 to 4 is 14-11 = 3.

This means that x increases by 3 when y increases by 1. Therefore, the relationship between x and y is x = 3y + k, where k is a constant.

To find the value of k, we can substitute the values of x and y from the first given condition:

11 = 3(3) + k
11 = 9 + k
k = 2

So, the relationship between x and y is x = 3y + 2.

Now, to find x when y=10:

x = 3(10) + 2
x = 30 + 2
x = 32

Therefore, when y=10, x=32.