To determine which line is parallel to the line \( y = 14x + 2 \), we need to identify the slope of this line. The slope-intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope.
In this case, the slope (m) of the line \( y = 14x + 2 \) is \( 14 \).
For two lines to be parallel, they must have the same slope. Let's check the slopes of the given options:
Option #1: \( y = 14x + 8 \)
- Slope is \( 14 \). (This line is parallel.)
Option #2: \( 4y = x + 8 \)
- Rearranging this gives:
\( y = \frac{1}{4}x + 2 \) - Slope is \( \frac{1}{4} \). (Not parallel.)
Option #3: \( y = 4x + 2 \)
- Slope is \( 4 \). (Not parallel.)
Option #4: \( y = -4x + 8 \)
- Slope is \( -4 \). (Not parallel.)
The line in Option #1 \( y = 14x + 8 \) is parallel to the given line.
So, the answer is:
The line in Option #1 is parallel to the given line.