Which of the following is a linear function?(1 point)

To determine which of the given equations is a linear function, we can evaluate each one:

1. **\( y = -12x + 78 \)**: This is in the form \( y = mx + b \), where \( m = -12 \) and \( b = 78 \). This is a linear function.

2. **\( y = -\frac{12}{x} + \frac{7}{8} \)**: This equation involves \( \frac{1}{x} \), which means it's not linear (it is a rational function).

3. **\( y = 2x^3 + 4 \)**: This involves \( x^3 \), which indicates it is a cubic function, not linear.

4. **\( 2y - 5x = 9 \)**: We can rearrange this into the form \( y = mx + b \):
\[
2y = 5x + 9 \\
y = \frac{5}{2}x + \frac{9}{2}
\]
This is also a linear function.

5. **\( x^2 + y = 33 \)**: This involves \( x^2 \), which indicates it is a quadratic function, not linear.

Thus, the options that represent linear functions are:

- \( y = -12x + 78 \)
- \( 2y - 5x = 9 \) (which can be rearranged to a linear form)

**Final Response**: **Both \( y = -12x + 78 \) and \( 2y - 5x = 9 \) are linear functions.**