Which is always a correct conclusion about the quantities in the function y=x+4
A. THe variable x is always 4 more than y
B. When the value of x is negative the value of y is also negative
C.The variable y is always greater than x
D.As the value of x increases the value of y decreases
B or C?
C probably.
TY
The correct conclusion about the quantities in the function y = x + 4 is option C: The variable y is always greater than x.
To see why, let's analyze the function. In the equation y = x + 4, the variable x represents any real number. When you substitute a value for x into the equation, you get the corresponding value for y.
For example, if we choose x = 0, then y = 0 + 4 = 4. This tells us that when x is 0, y is 4. Similarly, if we choose x = -3, then y = -3 + 4 = 1. This tells us that when x is -3, y is 1.
By looking at these examples and considering any other value of x, we can see that y is always greater than x. Therefore, the correct conclusion is that y is always greater than x (option C).
To determine which conclusion is correct about the quantities in the function y=x+4, let's analyze each option:
A. The variable x is always 4 more than y: This conclusion is not correct because in the function y=x+4, y is the dependent variable, meaning its value is determined by the value of x. Therefore, x is 4 more than y, not the other way around.
B. When the value of x is negative, the value of y is also negative: This conclusion is not always correct. If x is negative, but greater than -4, then y will be positive. For example, if x = -2, y = (-2) + 4 = 2, which is positive.
C. The variable y is always greater than x: This conclusion is always correct. In the function y=x+4, the coefficient of x is positive (1), indicating that as x increases, y will also increase. Therefore, y is always greater than x.
D. As the value of x increases, the value of y decreases: This conclusion is not correct. Since the coefficient of x is positive (1), as x increases, y will also increase.
Based on the analysis above, the correct conclusion about the quantities in the function y=x+4 is option C: The variable y is always greater than x.