Determine whether the graphs of the pair of lines are parallel. \( \begin{array}{l}x+13=y \\ y-x=-9\end{array} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line \( x+13=y \) is B. The slope of the line \( x+13=y \) is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. The slope of the line \( y-x=-9 \) is B. Are the graphs of the given equations parallel? Yes No

To determine whether the graphs of the pair of lines are parallel, we need to compare their slopes. Lines are parallel if they have the same slope. First, let's find the slope of each line. For the line \( x+13=y \), we can rewrite it in slope-intercept form \( y=mx+b \), where \( m \) is the slope and \( b \) is the y-intercept. \( x+13=y \) can be rewritten as \( y=x+13 \). So, the slope of the line \( x+13=y \) is \( m=1 \). Now, let's find the slope of the line \( y-x=-9 \). We can also rewrite this equation in slope-intercept form. \( y-x=-9 \) can be rewritten as \( y=x-9 \). So, the slope of the line \( y-x=-9 \) is \( m=1 \). Since both lines have the same slope of \( m=1 \), the graphs of the given equations are parallel. Now, let's fill in the answer boxes: A. The slope of the line \( x+13=y \) is \( 1 \). B. The slope of the line \( y-x=-9 \) is \( 1 \). Are the graphs of the given equations parallel? Yes