Algorithm - Help

[NeoDeGenero]

i'm kinda stuck on a concept.
Basically,
i want to do this:

I am given a Xmin Ymin, Xmax Ymax, and 3 sets of Coords to make a triangle.

Sounds simple enough,
however, this triangle must fit into a Row x Column grid.
The X and Y limits and the coords can be float and/or negative.

I have attempted to solve the placements of the coordinates by applying the y = mx + b formula.

Since basically, i want to scale Xmin Ymin Xmax Ymax to Row and Column Scale.

Eg. Row = 7, Col = 11
Xmin = -1
Xmax = 1
Ymin = 0
Ymax = 1

if i have three coordinates

(-0.4, 0) (0.95, 1) (-1, 0.33)

you should get something like this:

(each - is a column, and each | is a row)

for floats:
row: 7
column: 11
xmin: -1
xmax: 1
ymin: 0
ymax: 1
coords1: (-0.4, 0)....1
coords2: (0.95, 1)....2
coords3: (-1, 0.33)...3
  

y range = 0 to 1
 ^----------- ^
6|           |
5|        2  |
4|           |
3|           |
2| 3         |
1|           |
0|   1       |
 ^-----------^
  0123456789a

x range -1 to 1
where a = 10

My problem is now, how do i scale it accordingly?

the way i attempted it was,
i have a Xmin to Xmax of -1 to 1, on 11 columns.

1 |
0 |
-1|______
..1 to 11

so by using y = mx + b
b (intercept) = -1
m (gradient) = rise/run = 2/11
x = (y-b)/m


so by applying that formula,
i should be able to get the corresponding value in the 1 to 11 scale.

similarly for the scale of 1 to 7,
where m = 2/7

Doing paper calculations,
for the coords to new coords

coords1: (-0.4, 0) => (3.3, 0) supposed to be (3,0)
coords2: (0.95, 1) => (10.7, 7.7) supposed to be (8,5)
coords3: (-1, 0.33) => (0, 2.31) supposed to be (1,2)

the same is applied for :
row: 5
column: 7
xmin: 0
xmax: 12
ymin: 0
ymax: 12
coords1: (1, 2) =>(0.58, 0.8), supposed to be(1,1)
coords2: (6, 10) =>(3.5, 4.1), supposed to be(3,3)
coords3: (11, 2) => (6.41, 0.8), supposed to be(5,1)

for ints:


row: 5
column: 7
xmin: 0
xmax: 12
ymin: 0
ymax: 12
coords1: (1, 2)....1
coords2: (6, 10)...2
coords3: (11, 2)...3

 ^-------^
4|       |
3|   2   |
2|       |
1| 1   3 |
0|       |
 ^-------^
  0123456

the coords are not the same as it should be.



Help plz ><

edit:
bad code tag,