In which choice is \( y \) a linear function of \( x \) ? A \( y=\sqrt{x-4}+5 \) B \( \quad y=\frac{2}{x-3} \) C \( y=7 x(x+8) \) D \( y=\frac{9-x}{6^{2}} \)

We want to find the function where y is a linear function of x; that is, it can be written in the form y = mx + b. Choice A: y = √(x - 4) + 5 • The square root prevents this from being a linear function. Choice B: y = 2/(x - 3) • This is a rational function, not linear. Choice C: y = 7x(x + 8) • Expanding gives y = 7x² + 56x, which is quadratic (not linear). Choice D: y = (9 - x)/(6²) • First, note that 6² = 36. So this can be rewritten as:   y = (9 - x)/36 = (-x/36) + (9/36)   y = (-1/36)x + 1/4 This is in the form y = mx + b, with m = -1/36 and b = 1/4, hence a linear function. Answer: Choice D is the linear function.