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

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To determine which equation represents a line perpendicular to line $$ p $$, let's follow these steps:

1. **Find the slope of line $$ p $$:**
   
   Line $$ p $$ passes through the points $$ (9,7) $$ and $$ (13,5) $$.

$$
   \text{Slope of } p, m_p = \frac{5 - 7}{13 - 9} = \frac{-2}{4} = -\frac{1}{2}
   $$

2. **Determine the slope of the perpendicular line:**
   
   The slope of a line perpendicular to $$ p $$ is the negative reciprocal of $$ -\frac{1}{2} $$, which is:

$$
   m_{\perp} = 2
   $$

3. **Identify the equation with this slope:**
   
   Among the given options, the equation with a slope of $$ 2 $$ is:

$$
   y = 2x - 11
   $$

This equation has the required slope and thus represents a line perpendicular to line $$ p $$.

**Answer:** $$ y=2 x-11 $$
The equation $$ y = 2x - 11 $$ is perpendicular to line $$ p $$.

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

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