To find a line that is parallel to the line given by the equation \(y = 2x + 4\), we need to remember that parallel lines have the same slope.
The slope of the given line \(y = 2x + 4\) is \(2\).
Now, let's analyze the options to find which line has the same slope:
A. \(y = -2x + 2\) (slope = -2)
B. \(y = -\frac{1}{2}x + 4\) (slope = -\frac{1}{2})
C. \(y = 2x - 7\) (slope = 2)
D. \(y = \frac{1}{2}x - 3\) (slope = \frac{1}{2})
The only option with the same slope as \(2\) is:
C. \(y = 2x - 7\)
So, the correct answer is C.