Y is partly constant and partly varies as x, when x=1, y=7 and when x=2, y=11 find the equation connecting x and y
y = ax + b
so
a+b = 7
2a+b = 11
Now just solve for a and b
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To find the equation connecting x and y, we need to determine the part of y that is constant and the part that varies with x.
Let's start by finding the constant part of y. We are given that when x=1, y=7. This means that when x=1, the constant part of y is 7.
Now, let's find the part of y that varies with x. We are also given that when x=2, y=11. This means that when x=2, the variable part of y is 11-7 = 4.
To find the equation connecting x and y, we can write it as:
y = constant part + variable part
Substituting the values we found:
y = 7 + 4(x-1)
Simplifying the equation:
y = 7 + 4x - 4
y = 4x + 3
Therefore, the equation connecting x and y is y = 4x + 3.
To find the equation connecting the variables x and y, we need to determine the part of y that remains constant and the part that varies with x.
Given that y is partly constant and partly varies as x, let's first determine the constant part. We know that when x=1, y=7. This means that when x=1, the constant part of y is 7.
To find the part of y that varies with x, we'll subtract the constant part from the value of y when x=2. When x=2, y=11. Therefore, the part of y that varies with x is 11 - 7 = 4.
Now, to form the equation connecting x and y, we can write it as:
y = (constant part) + (varying part)
Substituting the values we found, the equation becomes:
y = 7 + 4x
So, the equation connecting x and y is y = 7 + 4x.