How would you solve this algebra problem

Someone please explain in detail how to solve this problem.
Which line does NOT intersect the line passing through the points (-15,7) and (5,-18)?

A. 4x-5y=10
B. 8x+10y=10
C. 10x-8y=10
D. 15x+12y=10

Slope = (y2-y1)/(x2-x1)
= (-18-7)/(5-(-15))
= -25/(5+15)
= -25/20
= -5/4
The slope of this line is -5/4. A line that is a parallel to it would never intersect it. A parallel line would have the same slope, also -5/4.

Choice A:
4x-5y = 10
4x-5y-4x = 10-4x
-5y = 10-4x
-5y = -4x+10
-5y/-5 = (-4x+10)/-5
y = (4/5)x-2
The slope of this line is 4/5. It is not parallel to our line.

Choice B:
8x+10y = 10
8x+10y-8x = 10-8x
10y = 10-8x
10y = -8x+10
10y/10 = (-8x+10)/10
y = (-4/5)x+1
The slope of this line is -4/5. It is not parallel to our line.

Choice C:
10x-8y = 10
10x-8y-10x = 10-10x
-8y = 10-10x
-8y = -10x+10
-8y/-8 = (-10x+10)/-8
y = (5/4)x-(5/4)
The slope of this line is 5/4. It is not parallel to our line.

Choice D:
15x+12y = 10
15x+12y-15x = 10-15x
12y = 10-15x
12y = -15x+10
12y/12 = (-15x+10)/12
y = (-5/4)x+(5/6)
The slope of this line is -5/4. It is, in fact, parallel to our line.

Answer: D