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 slope of a line in the equation form Ax + By = C, we solve for y to rewrite the equation in slope-intercept form (y = mx + b), where m is the slope. 1. For the equation 2x + 5y = 2: • Subtract 2x from both sides:   5y = –2x + 2 • Divide every term by 5:   y = –(2/5)x + 2/5 • Thus, the slope (m) is –2/5. Since Option A asks for the slope of 2x + 5y = 2, the correct selection is: A. The slope of 2x + 5y = 2 is –2/5. 2. Next, examine the second equation 4x + 10y = 1: • Subtract 4x from both sides:   10y = –4x + 1 • Divide every term by 10:   y = –(4/10)x + 1/10, which simplifies to:   y = –(2/5)x + 1/10 • The slope is also –2/5. Both lines have the same slope (–2/5) but different y-intercepts. Hence, the two lines are parallel. Final Answer: A. The slope of 2x+5y=2 is –2/5, and the two lines are parallel.