The equations of three lines are given below. Line $1: y=-2 x+3$ Line $2: y=-2 x-4$ Line $3: 3 x-6 y=6$ 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 equations of three lines: Line 1: \(y=-2x+3\), Line 2: \(y=-2x-4\), and Line 3: \(3x-6y=6\).

Step 2 ：We need to determine whether each pair of lines are parallel, perpendicular, or neither.

Step 3 ：Two lines are parallel if their slopes are equal. Two lines are perpendicular if the product of their slopes is -1. If neither of these conditions are met, the lines are neither parallel nor perpendicular.

Step 4 ：First, we find the slopes of the three lines. For Line 1 and Line 2, the slopes are -2 and -2 respectively, which can be directly read from the equations as they are in the slope-intercept form \(y = mx + b\), where \(m\) is the slope.

Step 5 ：For Line 3, we need to rearrange the equation into the slope-intercept form to find the slope. The slope of Line 3 is 1/2.

Step 6 ：Now we can compare the slopes of each pair of lines to determine whether they are parallel, perpendicular, or neither.

Step 7 ：\(\boxed{\text{Final Answer: Line 1 and Line 2: Parallel, Line 1 and Line 3: Neither, Line 2 and Line 3: Neither}}\)