Y is partly constant and partly varies as x and when x=5,y=8 and when x=6,y=4.Find the equation connecting y and x
y = mx + b
so,
5m+b = 8
6m+b = 4
so solve for m and b
looks like our classical
y = mx + b
using (5,8)
8 = 5m + b **
using (6,4)
4 = 6m + b ***
subtract *** from ** and find m
once you have m you can find b
To find the equation connecting y and x, let's break down the information provided:
We are given that y is partly constant and partly varies with x. This means that there is a constant part of y and a variable part of y that depends on x.
Given the values of (x, y) as (5, 8) and (6, 4), we can determine the constant part of y and the variable part of y.
When x = 5, y = 8. This means that the constant part of y is 8.
When x = 6, y = 4. This means that the decrease in y from the constant part is 8 - 4 = 4.
Since the variable part of y decreases by 4 when x increases by 1, we can express the variable part of y as -4x. Thus, the equation connecting y and x is:
y = 8 - 4x
To find the equation connecting y and x, we need to determine the constant part and the variable part in the relationship between them.
Given that y is partly constant and partly varies as x, we can express this as:
y = constant + variable
Let's determine the constant part of y. We know that when x = 5, y = 8. So, substituting these values into the equation:
8 = constant + (variable)(5)
Now, let's determine the variable part of y. We also know that when x = 6, y = 4. Substituting these values into the equation:
4 = constant + (variable)(6)
We now have a system of two equations:
8 = constant + 5(variable) --(1)
4 = constant + 6(variable) --(2)
To find the values of the constant and variable, we can solve this system of equations simultaneously.
Subtracting equation (2) from equation (1), we get:
8 - 4 = constant + 5(variable) - (constant + 6(variable))
4 = -1(variable)
variable = -4
Substituting the value of the variable into equation (1), we get:
8 = constant + 5(-4)
8 = constant - 20
constant = 28
Now that we have the values of the constant and variable, we can write the equation connecting y and x:
y = 28 - 4x
Therefore, the equation connecting y and x is y = 28 - 4x.