Which equation does not represent y as a function of x?
A. -7y = 2
B. 6x = -8y
C. 5y^2 + 2x = -4
D. 4x^2 + 9y = -8
Look at C. Is there one y for each x?
To determine which equation does not represent y as a function of x, we need to check if each equation can be rewritten in the form y = f(x), where f(x) is some expression involving x.
Let's analyze each option:
A. -7y = 2
To check if y is a function of x, we need to isolate y on one side of the equation. Dividing both sides by -7, we have:
y = -2/7
This equation can be rewritten as y = f(x), where f(x) = -2/7. Therefore, option A represents y as a function of x.
B. 6x = -8y
Again, we isolate y to see if it can be expressed as a function of x. Dividing both sides by -8, we get:
y = -3/4x
This equation can be rewritten as y = f(x), where f(x) = -3/4x. Therefore, option B represents y as a function of x.
C. 5y^2 + 2x = -4
Here, we have y squared, which means y cannot be isolated as a function of x. Taking the square root of both sides would result in a positive and negative value of y, breaking the definition of a function. Therefore, option C does not represent y as a function of x.
D. 4x^2 + 9y = -8
In this equation, we cannot isolate y as a function of x. Taking the square root of both sides would once again result in a positive and negative value of y. Therefore, option D does not represent y as a function of x.
In conclusion, the equation that does not represent y as a function of x is C. 5y^2 + 2x = -4.