Which equation represents a linear function? \( \begin{array}{ll}\text { A } y=\frac{3}{x}-4 & \text { B } y=3 x^{2}-4 x+5 \\ \text { C } y=8-3 x & \text { D } x=-3\end{array} \)

To determine which equation represents a linear function, we need to identify the form of each equation. A linear function can be expressed in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Let's analyze each option: - **Option A:** \( y = \frac{3}{x} - 4 \) This is not a linear function because it contains a term with \( x \) in the denominator, which makes it a rational function. - **Option B:** \( y = 3x^2 - 4x + 5 \) This is a quadratic function because of the \( x^2 \) term. It is not linear. - **Option C:** \( y = 8 - 3x \) This can be rewritten as \( y = -3x + 8 \), which is in the form \( y = mx + b \). Therefore, this is a linear function. - **Option D:** \( x = -3 \) This represents a vertical line, which is not a function in the context of \( y \) being expressed in terms of \( x \). Based on this analysis, the equation that represents a linear function is: **C:** \( y = 8 - 3x \)