Real quick about to turn in ( show work )

1. y - y1 = m(x - x1)
slope(m) = -1/3
(3,6)...x1 = 3 and y1 = 6
now we sub
y - 6 = -1/3(x - 3) <==

2. y - 9 = -(x + 2)
y - 9 = -x - 2
y = -x - 2 + 9
y = -x + 7 <===

3. y - y1 = m(x - x1)
    slope(m) = 0horizontal lines have 0 slopes
    (-4,-1)...x1 = -4 and y1 = -1
  now we sub
    y - (-1) = 0(x - (-4)
    y + 1 = 0(x + 4) <===

4. x + 3y = 6
     3y = -x + 6
     y = -1/3x + 2slope here is -1/3. A parallel line will have the same slope

y = mx + b
slope(m) = -1/3
(5,3)...x = 5 and y = 3
now we sub and find b, the y int
3 = -1/3(5) + b
3 = -5/3 + b
3 + 5/3 = b
9/3 + 5/3 = b
14/3 = b
ur equation is : y = -1/3x + 14/3

5. Perpendicular lines have negative reciprocal slopes. For example : the slope of one line will be 3 and the slope of the other line would be -1/3.

(-1,-4) / (3,3)
slope = (3 - (-4) / (3 - (-1) = (3 + 4) / (3 + 1) = 7/4

that means our other line has to have slope of -4/7, the negative reciprocal

(-3,3)(4,-1)
slope = (-1 - 3) / (4 - (-3) = -4/7

so ur answer is (4,-1)