Identify Linear Functions: Examining y = mx + b Properties

To solve this problem, we'll examine each expression to see if it represents a linear function:

• Option A: $y = 5 - 3x$.
  This expression fits the linear form $y = mx + c$ with $m = -3$ and $c = 5$. Hence, it is a linear function.
• Option B: $y = -4(x+1) + 4x$.
  First, expand the expression:
  $-4(x+1) = -4x - 4$.
  Substituting, we get $y = -4x - 4 + 4x$, which simplifies to $y = -4$.
  This is a linear function where $y = c$ (a constant term with zero slope).
• Option C: $y = -3x^2 + 2$.
  The term $-3x^2$ indicates a quadratic expression, as the highest power of $x$ is 2. Therefore, it is not a linear function.
• Option D: $y = 6 + x^3$.
  The term $x^3$ shows a cubic expression since the highest power of $x$ is 3, thus not a linear function.

Clearly, only options A and B describe linear functions. Therefore, the correct answer is:

Answers A and B are correct.