To find a line that is parallel to the line given by the equation \( y = 2x + 4 \), we need to identify another line that has the same slope. The slope of the given line is \( 2 \).
Now, let's examine each option to find out which one has the same slope:
a. \( y = 2x - 7 \) → Slope is \( 2 \) (This is parallel)
b. \( y = -2x + 2 \) → Slope is \( -2 \)
c. \( y = -\frac{1}{2}x + 4 \) → Slope is \( -\frac{1}{2} \)
d. \( y = \frac{1}{2}x - 3 \) → Slope is \( \frac{1}{2} \)
The only equation that has the same slope of \( 2 \) is:
a. \( y = 2x - 7 \)
So, the correct answer is a. y = 2x - 7.