Suppose we are given the following. Line 1 passes through $(6,2)$ and $(3,0)$. Line 2 passes through $(2,-2)$ and $(6,4)$. Line 3 passes through $(-2,-1)$ and $(0,2)$. (a) Find the slope of each line. Slope of Line $1=$ Slope of Line $2=$ Slope of Line $3=$ (b) For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2: Line 1 and Line 3 : Line 2 and Line 3 : Parallel Parallel Parallel Perpendicular Perpendicular Perpendicular Neither Neither Neither

Step 1 ：Given the points through which each line passes, we can calculate the slope of each line using the formula \((y2 - y1) / (x2 - x1)\), where \((x1, y1)\) and \((x2, y2)\) are the coordinates of two points on the line.

Step 2 ：For Line 1, which passes through the points \((6, 2)\) and \((3, 0)\), the slope is calculated as \((0 - 2) / (3 - 6) = 0.67\).

Step 3 ：For Line 2, which passes through the points \((2, -2)\) and \((6, 4)\), the slope is calculated as \((4 - (-2)) / (6 - 2) = 1.5\).

Step 4 ：For Line 3, which passes through the points \((-2, -1)\) and \((0, 2)\), the slope is calculated as \((2 - (-1)) / (0 - (-2)) = 1.5\).

Step 5 ：So, the slopes of the lines are: Slope of Line 1 = \(\boxed{0.67}\), Slope of Line 2 = \(\boxed{1.5}\), Slope of Line 3 = \(\boxed{1.5}\).

Step 6 ：Next, we compare the slopes of each pair of lines to determine whether they are parallel, perpendicular, or neither. Two lines are parallel if their slopes are equal, they are perpendicular if the product of their slopes is -1, and they are neither if neither of these conditions is met.

Step 7 ：Comparing Line 1 and Line 2, the slopes are not equal and their product is not -1, so they are neither parallel nor perpendicular.

Step 8 ：Comparing Line 1 and Line 3, the slopes are not equal and their product is not -1, so they are neither parallel nor perpendicular.

Step 9 ：Comparing Line 2 and Line 3, the slopes are equal, so they are parallel.

Step 10 ：Thus, for each pair of lines: Line 1 and Line 2: \(\boxed{\text{Neither}}\), Line 1 and Line 3 : \(\boxed{\text{Neither}}\), Line 2 and Line 3 : \(\boxed{\text{Parallel}}\).