To find an equation of a line that is parallel to the line given by the equation \( y = 2x + 4 \), we need to identify that parallel lines have the same slope.
The slope of the line \( y = 2x + 4 \) is \( 2 \). Therefore, any line that is parallel to this line must also have a slope of \( 2 \).
Now, let's examine the provided response options to find which equation has a slope of \( 2 \):
- \( y = -2x + 2 \) (slope = -2)
- \( y = 12x - 3 \) (slope = 12)
- \( y = \frac{1}{2}x - 3 \) (slope = \frac{1}{2})
- \( y = -12x + 4 \) (slope = -12)
- \( y = -\frac{1}{2}x + 4 \) (slope = -\frac{1}{2})
- \( y = 2x - 7 \) (slope = 2)
The only option that has a slope of \( 2 \) is:
\( y = 2x - 7 \)
Thus, this equation fits a line that is parallel to the line \( y = 2x + 4 \).