For the given pair of equations, give the slopes of the lines, and then determine whether the two lines are parallel, perpendicular, or neither. \( \begin{array}{l}2 x+5 y=2 \\ 4 x+10 y=1\end{array} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of \( 2 x+5 y=2 \) is (Type an integer or a simplified fraction.) B. The slope of \( 2 x+5 y=2 \) is undefined.

To find the slopes of the given lines, we first need to rewrite both equations in slope-intercept form (y = mx + b), where m is the slope. For the first equation, \( 2x + 5y = 2 \): 1. Rearranging gives us \( 5y = -2x + 2 \). 2. Dividing all terms by 5 results in \( y = -\frac{2}{5}x + \frac{2}{5} \). The slope of the first line is \( -\frac{2}{5} \). For the second equation, \( 4x + 10y = 1 \): 1. Rearranging gives us \( 10y = -4x + 1 \). 2. Dividing all terms by 10 results in \( y = -\frac{2}{5}x + \frac{1}{10} \). The slope of the second line is also \( -\frac{2}{5} \). Since both slopes are equal, the lines are parallel. A. The slope of \( 2x + 5y = 2 \) is \( -\frac{2}{5} \). B. The slope of \( 4x + 10y = 1 \) is also \( -\frac{2}{5} \). Thus, the lines are parallel!