intermediate algebra slope intercept and point slope form questions?

I'll explain this once so I don't have to repeat:
slope or gradient of any typical line, known as m, is given by: m = [y2 - y1] / [x2 - x1]
where you know two coordinates (x1,y1) and (x2,y2)
the y-intercept of any line is given by the value of c in equations of the form y = mx + c
and to get that y-intercept value you need to know the gradient and any one point on the line to plug those into the formula and solve for c

1)
m = (9 - 0) / (0 - (-3)) = 9 / 3 = 3
y = 3x + c
9 = 3(0) + c
9 = c
y = 3x + 9 in slope intercept form

2)
y = (-4/5)x + c
-5 = (-4/5)(5) + c
-5 = -4 + c
c = -5 - (-4) = -1
y = (-4/5)x - 1 in slope intercept form

3)
y = 3x + c
5 = 3(7) + c
5 = 21 + c
c = 5 - 21 = -16
y = 3x - 16 in slope intercept form

4)
slope = m = -8/9
y-intercept = c = 0
graph will go from top left to bottom right through the origin

5)
slope = m = 3
y-intercept = c = 6
graph will go from bottom left to top right, it will be fairly steep, it crosses the x-axis at (0,6) and the y-axis where (-2,0)

6)
m = (-9 - 7) / (1 - 5) = -16 / -4 = 4
y = 4x + c
7 = 4(5) + c
c = 7 - 20 = -13
y = 4x - 13 in slope intercept form
the line rises from bottom left to top right (the value of m is positive and non-zero)

7)
m = (4 - 6) / (4 - (-5)) = -2 / 9
y = -(2/9)x + c
4 = -(2/9)(4) + c
c = 4 + (8/9) = 44/9
y = -(2/9)x + (44/9) in slope intercept form
the line falls from top left to bottom right (the value of m is negative and non-zero)

8)
x + 2y = 6
2y = 6 - x = -x + 6
y = -(1/2)x + (1/2)6
y = -(1/2)x + 3
y-intercept = c = 3 at point (0,3)
x-intercept when y=0 => 0 = -(1/2)x + 3 => -(1/2)x = -3 => x = 6 at point (6,0)