x is partly constant and partly varies with y when y =5,x=19,and when y=10, x= 34
x = a + by
using the given points, you have
a+5b = 19
a+10b = 34
so, 5b=15
now finish it off.
Salut hhkdiv jjkg
To find the relationship between x and y, we can start by finding the constant part and the varying part.
Step 1: Find the constant part:
When y = 5, x = 19. This gives us a data point (5, 19).
Step 2: Find the varying part:
When y = 10, x = 34. This gives us another data point (10, 34).
Step 3: Find the difference in x values:
The difference between the x values (34 - 19 = 15) would represent the varying part.
Step 4: Find the difference in y values:
The difference between the y values (10 - 5 = 5) can be used to determine the constant part.
Step 5: Calculate the constant part:
We can divide the difference in x values by the difference in y values to find the constant rate of change:
Constant part = (34 - 19) / (10 - 5) = 15 / 5 = 3.
Step 6: Express the relationship between x and y:
We can express the relationship as:
x = constant part + varying part
x = 3y + 15
So, the relationship between x and y is x = 3y + 15, where 15 represents the constant part and 3 represents the varying part.
To determine the relationship between x and y, we can first find the constant part of x and the varying part of x.
Given that when y = 5, x = 19, we can consider this as the constant part of x. Therefore, x can be represented as:
x = constant + varying part
Substituting the values, we get:
19 = constant + varying part (equation 1)
Now, let's find the varying part of x. We have another set of values where y = 10 and x = 34. Substitute these values into the equation:
34 = constant + varying part (equation 2)
Now, we have a system of equations with two unknowns (constant and varying part) and two equations. We can solve this system to find the values of the unknowns.
To eliminate the constant, subtract equation 1 from equation 2:
34 - 19 = (constant + varying part) - (constant + varying part)
15 = varying part - varying part
15 = 0
This equation tells us that the varying part cancels out, which means the varying part is not present in this system. Therefore, the constant part of x is 15.
Substituting the constant part back into equation 1:
19 = 15 + varying part
To isolate the varying part, subtract 15 from both sides:
varying part = 19 - 15
varying part = 4
Now we have found that the constant part of x is 15 and the varying part is 4.
Therefore, the relationship between x and y can be expressed as:
x = 15 + 4y