Line \( p \) contains the points \( (9,7) \) and \( (13,5) \). Which equation represents a line perpendicular to line \( p \). \( \begin{array}{l}y=-1 / 2 x+1 \\ y=1 / 2 x+5 / 2 \\ y=2 x-11 \\ y=-2 x+31\end{array} \)

To find the slope of line \( p \) that passes through points \( (9, 7) \) and \( (13, 5) \), we can use the formula for the slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in our points gives us \( m = \frac{5 - 7}{13 - 9} = \frac{-2}{4} = -\frac{1}{2} \). The slope of a line perpendicular to line \( p \) is the negative reciprocal, which is 2. Now, let's see which equation corresponds to this slope. The equation \( y = 2x - 11 \) has a slope of 2, making it the equation we are looking for! So, the equation that represents a line perpendicular to line \( p \) is \( y = 2x - 11 \).