Questions: Consider the following relation. 3 x+y=-4 x-3 y Step 1 of 3: Rewrite the relation as a function of x. Answer 0.33 Points f(x)=

Solution Steps

To rewrite the given relation as a function of \( x \), we need to solve the equation for \( y \) in terms of \( x \). This involves isolating \( y \) on one side of the equation.

1. Combine like terms involving \( x \) and \( y \) on each side of the equation.
2. Move all terms involving \( y \) to one side and all terms involving \( x \) to the other side.
3. Solve for \( y \) to express it as a function of \( x \).

We start with the equation: \[ 3x + y = -4x - 3y \] To isolate \( y \), we first rearrange the equation by moving all terms involving \( y \) to one side and all terms involving \( x \) to the other side: \[ 3x + y + 3y = -4x \] This simplifies to: \[ 3x + 4y = -4x \] Next, we combine like terms: \[ 4y = -4x - 3x \] This results in: \[ 4y = -7x \] Now, we divide both sides by 4 to solve for \( y \): \[ y = -\frac{7}{4}x \]

Final Answer