Suppose we are given the following. Line 1 passes through (-3,-2) and (-1,4) Line 2 passes through (0,1) and (-1,-2) Line 3 passes through (-6,-3) and (3,-6) (a) Find the slope of each line. Slope of Line1=square Slope of Line2=square Slope of Line3=square (b) For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither

(a) To find the slope of each line, we can use the formula:

Slope = (y2 - y1) / (x2 - x1)

For Line 1:
Slope of Line 1 = (4 - (-2)) / ((-1) - (-3))
Slope of Line 1 = 6 / 2
Slope of Line 1 = 3

For Line 2:
Slope of Line 2 = (1 - (-2)) / (0 - (-1))
Slope of Line 2 = 3 / 1
Slope of Line 2 = 3

For Line 3:
Slope of Line 3 = (-6 - (-3)) / (3 - (-6))
Slope of Line 3 = -3 / 9
Slope of Line 3 = -1/3

(b) To determine whether the lines are parallel, perpendicular, or neither, we can compare their slopes.

Line 1 and Line 2:
Since the slopes of Line 1 and Line 2 are both 3, they are parallel.

Line 1 and Line 3:
The slopes of Line 1 and Line 3 are 3 and -1/3, respectively. Since the product of their slopes is not equal to -1, they are neither parallel nor perpendicular.

Line 2 and Line 3:
The slopes of Line 2 and Line 3 are both 3, so they are parallel.

Therefore, the answers are:
(a) Slope of Line 1 = 3, Slope of Line 2 = 3, Slope of Line 3 = -1/3
(b) Line 1 and Line 2: Parallel, Line 1 and Line 3: Neither, Line 2 and Line 3: Parallel