Algebra, I need help finding the X and Y intercept along with the Slope.

I need help finding the X and Y intercept and the Slope, it's confusing me because some of these don'y have x values, and some don't have Y values. I need help finding the X and Y value and slope for the following equations:

5x - 12y = 10

3y + 9 = 15

5x - 2y = 10 - 2y

5x - 12y = 10

when y = 0
5x = 10
x = 2
(2, 0)

when x = 0
-12y = 10
y = -10/12
y = -5/6
(0, -5/6)

solve for y to put the equation in slope intercept form y = mx + b where m is the slope
5x - 12y = 10
-12y = -5x + 10
y = (5/12)x - 10/12
m = 5/12


3y + 9 = 15
3y = 6
y = 2

this is a horizontal line with a slope of 0 and a y intercept of (0, 2)

5x - 2y = 10 - 2y
5x = 10
x = 2

this is a vertical line with an undefined sloped and a x intercept of (2, 0)

3y+9=15, 3y=6, y=2, so no matter what x equals for that problem, y will always be 2

5x-2y=10-2y, 5x=10, x=2, so no matter what y equals for that problem, x will always be 2